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A pond's depth at one end is twice as deep as the other end. Eighteen inches are drained and as a result, the deep end is 3 times as deep as the shallow end. Calculate original depths.
Answers provided with problem: 36 inches, 72 inches.
Let D = deep end.
Let S = shallow end.
D = 2S
D = 3S - 18
How do I solve ?
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Original Depths: Deep and Shallow Parts
16 posts
• Page 1 of 1
Re: Original Depths: Deep and Shallow Parts
by Guest » Sun May 08, 2016 7:52 am
Let D = deep end.
Let S = shallow end.
Let D2 = deep end.after 18 drained
Let S2 = shallow end. after 18 drained
D = 2S
D2 = 2S -18
S2 = S - 18
D2 = 2S - 18 .....you are told this is 3 times the shallow end when 18 ins drained so ... 3( S-18)
Let S = shallow end.
Let D2 = deep end.after 18 drained
Let S2 = shallow end. after 18 drained
D = 2S
D2 = 2S -18
S2 = S - 18
D2 = 2S - 18 .....you are told this is 3 times the shallow end when 18 ins drained so ... 3( S-18)
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Sun May 08, 2016 11:48 am
I thought I understood how to solve, but I don't.
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Sun May 08, 2016 2:20 pm
This is the outline of the solution I gave in my last post...........
..................
Let D = deep end.
Let S = shallow end.
Let D2 = deep end.after 18 drained
Let S2 = shallow end. after 18 drained
D = 2S
D2 = 2S -18
S2 = S - 18
D2 = 2S - 18 .....you are told this is 3 times the shallow end when 18 ins drained so ... 3( S-18)
..........................
I thought I understood how to solve, but I don't..........this is your last post.....what do you not understand.?....
what did you actually do to try and solve it..???
..................
Let D = deep end.
Let S = shallow end.
Let D2 = deep end.after 18 drained
Let S2 = shallow end. after 18 drained
D = 2S
D2 = 2S -18
S2 = S - 18
D2 = 2S - 18 .....you are told this is 3 times the shallow end when 18 ins drained so ... 3( S-18)
..........................
I thought I understood how to solve, but I don't..........this is your last post.....what do you not understand.?....
what did you actually do to try and solve it..???
- Guest
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Sun May 08, 2016 8:28 pm
I don't understand how you can be attempting to do questions like this without having some knowledge of algebra.
What knowledge of algebra do you have..??
Do you understand the steps taken so far..??
How did you manage to attempt the first step on your first post..??
What were you trying to do when you wrote down the first step you took..?
Can you explain in english what you are trying to do in the first step..?
And then explain in english what you think the next step may be..?
Can you explain in english what the following steps I posted are doing..?
You may not be able to do it mathematically, but can you explain it in english..??
If you don't know what you are doing and cannot explain it is a bit like saying "the room is dark" and having no knowledge of why it is dark.....
Is it dark because it in night time and everywhere else is dark also...?
Is it dark because the light has gone out, why has the light gone out, did someone switch it off, is there a fault with the light...???
Maybe the room appears dark because you cannot see, Why can you not see..??.... Have you your eyes closed...?? Is the room full of smoke...??
Regards the maths problem....you need to be able to say what you do not understand. Then someone can help you with the bits you do not understand.
If you do not understand anything about the problem then you would need to start at the very beginning and study the basics of algebra before attempting to do word problems like this.
What knowledge of algebra do you have..??
Do you understand the steps taken so far..??
How did you manage to attempt the first step on your first post..??
What were you trying to do when you wrote down the first step you took..?
Can you explain in english what you are trying to do in the first step..?
And then explain in english what you think the next step may be..?
Can you explain in english what the following steps I posted are doing..?
You may not be able to do it mathematically, but can you explain it in english..??
If you don't know what you are doing and cannot explain it is a bit like saying "the room is dark" and having no knowledge of why it is dark.....
Is it dark because it in night time and everywhere else is dark also...?
Is it dark because the light has gone out, why has the light gone out, did someone switch it off, is there a fault with the light...???
Maybe the room appears dark because you cannot see, Why can you not see..??.... Have you your eyes closed...?? Is the room full of smoke...??
Regards the maths problem....you need to be able to say what you do not understand. Then someone can help you with the bits you do not understand.
If you do not understand anything about the problem then you would need to start at the very beginning and study the basics of algebra before attempting to do word problems like this.
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Sun May 08, 2016 10:03 pm
" What knowledge of algebra do you have..?? I have been out of school 40 yrs. and am relearning on my own.
Do you understand the steps taken so far..?? Partially.
How did you manage to attempt the first step on your first post..?? I guessed.
What were you trying to do when you wrote down the first step you took..? Giving something for the deep and shallow ends.
Can you explain in english what you are trying to do in the first step..? The deep end is twice as deep as the shallow end: D = 2S
And then explain in english what you think the next step may be..? 18 inches are drained: minus 18
Can you explain in english what the following steps I posted are doing..? I don't know why you said D2 and S2.
You may not be able to do it mathematically, but can you explain it in english..?? " After draining the deep end is 3 times the shallow end.
Do you understand the steps taken so far..?? Partially.
How did you manage to attempt the first step on your first post..?? I guessed.
What were you trying to do when you wrote down the first step you took..? Giving something for the deep and shallow ends.
Can you explain in english what you are trying to do in the first step..? The deep end is twice as deep as the shallow end: D = 2S
And then explain in english what you think the next step may be..? 18 inches are drained: minus 18
Can you explain in english what the following steps I posted are doing..? I don't know why you said D2 and S2.
You may not be able to do it mathematically, but can you explain it in english..?? " After draining the deep end is 3 times the shallow end.
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Mon May 09, 2016 6:53 am
Yes, Good, You have explained your thinking well.... I will deal with each point in turn......
" What knowledge of algebra do you have..?? I have been out of school 40 yrs. and am relearning on my own.
Ok, not easy on your own, but with internet access and forums like this there is lots of help. If you don't know the very basics then you should start with the basics, simplifying basic algebra expressions, factorising expressions, and solving simple equations that are already set out. With questions like this one you have to understand in english what the problem itself is and then express it mathematically in the form of the unknowns, related expressions and equations
Do you understand the steps taken so far..?? Partially....... try and be more explicit when describing what you know and don't know.
How did you manage to attempt the first step on your first post..?? I guessed....... I don't think you really just guessed......I reckon you read the question and figured out there was a deep end to the pool that you let equal "D" and a shallow end that you let equal "S". These are what is known in algebra as the "unknowns" or the things you have to find. If there is only one unknown it can be solved by one equation. So you would have to derive only one equation from the information given in the question. This question is slightly more complicated in that there are 2 unknowns...the deep end depth "D" and the shallow end depth "S"......But...... the question tells us that they are related.......the deep end is twice the depth of the shallow end. We were told that in the first sentence of the question. What you did in the first step was to express this descriptive information given in the form of an english sentence as a mathematical sentence eg. an expression with the unknowns and equations to relate one to another.
What were you trying to do when you wrote down the first step you took..? Giving something for the deep and shallow ends. ...Yes, let some algebraic symbol represent the unknowns....ok
Can you explain in english what you are trying to do in the first step..? The deep end is twice as deep as the shallow end: D = 2S .....Yes, the question told us this fact......you have it now in the form of an equation relating the depth of the deep end to the depth of the shallow end.
And then explain in english what you think the next step may be..? 18 inches are drained: minus 18 ......Yes, 18 inches are drained, sot subtract 18 from each end of the pool....ok...... Now we are told the relationship between the deep end and the shallow end is no longer twice.....The deep end is now 3 times the depth at the shallow end. so we need to relate this new information in the form of another equation.
Can you explain in english what the following steps I posted are doing..? I don't know why you said D2 and S2. ......I just let D2 be the depth of deep end after 18 inches drained and S2 be the depth of the shallow end......not really required except we can say....
D2 = (D - 18)
S2 = (S - 18)
D = 2S ....the original relationship when pool is full
D2 = 3 x S2 .... the new relationship when pool drained 18 inches
You may not be able to do it mathematically, but can you explain it in english..?? " After draining the deep end is 3 times the shallow end. ......Yes, this is the english description ..... and we need to describe it mathematically as in previous paragraph.
From above we have ..........
D = 2S
D2 = (D - 18)
We have 2 unknowns, but they are related by D = 2S. The idea is to use substitution to substitute "2S" where we have a "D"
So instead of (D - 18) I can write (2S -18)
so that gives me ... D2 = 2S -18 ...this gives me the new "deep end" depth in terms of the original depth "S" of the "shallow end"
S2 = S - 18 ...... this is the new "shallow end" in terms of the original depth "S" of the shallow end. S now we know both ends in terms of "S" only.
.....you are told (D2) is 3 times (S2) so 3 times the shallow end when 18 ins drained so ... 3( S-18) is equal to (D2) which is (2S -18)
This is how we arrived at this in an earlier post.... D2 = 2S - 18 .....you are told this is 3 times the shallow end when 18 ins drained so ... 3( S-18)
So that means 2S - 18 = 3(S - 18)
This is a simple equation with one unknown "S" and can be solved by simple algebra........Have a go at it.....and post what you do........
" What knowledge of algebra do you have..?? I have been out of school 40 yrs. and am relearning on my own.
Ok, not easy on your own, but with internet access and forums like this there is lots of help. If you don't know the very basics then you should start with the basics, simplifying basic algebra expressions, factorising expressions, and solving simple equations that are already set out. With questions like this one you have to understand in english what the problem itself is and then express it mathematically in the form of the unknowns, related expressions and equations
Do you understand the steps taken so far..?? Partially....... try and be more explicit when describing what you know and don't know.
How did you manage to attempt the first step on your first post..?? I guessed....... I don't think you really just guessed......I reckon you read the question and figured out there was a deep end to the pool that you let equal "D" and a shallow end that you let equal "S". These are what is known in algebra as the "unknowns" or the things you have to find. If there is only one unknown it can be solved by one equation. So you would have to derive only one equation from the information given in the question. This question is slightly more complicated in that there are 2 unknowns...the deep end depth "D" and the shallow end depth "S"......But...... the question tells us that they are related.......the deep end is twice the depth of the shallow end. We were told that in the first sentence of the question. What you did in the first step was to express this descriptive information given in the form of an english sentence as a mathematical sentence eg. an expression with the unknowns and equations to relate one to another.
What were you trying to do when you wrote down the first step you took..? Giving something for the deep and shallow ends. ...Yes, let some algebraic symbol represent the unknowns....ok
Can you explain in english what you are trying to do in the first step..? The deep end is twice as deep as the shallow end: D = 2S .....Yes, the question told us this fact......you have it now in the form of an equation relating the depth of the deep end to the depth of the shallow end.
And then explain in english what you think the next step may be..? 18 inches are drained: minus 18 ......Yes, 18 inches are drained, sot subtract 18 from each end of the pool....ok...... Now we are told the relationship between the deep end and the shallow end is no longer twice.....The deep end is now 3 times the depth at the shallow end. so we need to relate this new information in the form of another equation.
Can you explain in english what the following steps I posted are doing..? I don't know why you said D2 and S2. ......I just let D2 be the depth of deep end after 18 inches drained and S2 be the depth of the shallow end......not really required except we can say....
D2 = (D - 18)
S2 = (S - 18)
D = 2S ....the original relationship when pool is full
D2 = 3 x S2 .... the new relationship when pool drained 18 inches
You may not be able to do it mathematically, but can you explain it in english..?? " After draining the deep end is 3 times the shallow end. ......Yes, this is the english description ..... and we need to describe it mathematically as in previous paragraph.
From above we have ..........
D = 2S
D2 = (D - 18)
We have 2 unknowns, but they are related by D = 2S. The idea is to use substitution to substitute "2S" where we have a "D"
So instead of (D - 18) I can write (2S -18)
so that gives me ... D2 = 2S -18 ...this gives me the new "deep end" depth in terms of the original depth "S" of the "shallow end"
S2 = S - 18 ...... this is the new "shallow end" in terms of the original depth "S" of the shallow end. S now we know both ends in terms of "S" only.
.....you are told (D2) is 3 times (S2) so 3 times the shallow end when 18 ins drained so ... 3( S-18) is equal to (D2) which is (2S -18)
This is how we arrived at this in an earlier post.... D2 = 2S - 18 .....you are told this is 3 times the shallow end when 18 ins drained so ... 3( S-18)
So that means 2S - 18 = 3(S - 18)
This is a simple equation with one unknown "S" and can be solved by simple algebra........Have a go at it.....and post what you do........
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Mon May 09, 2016 12:04 pm
2S - 18 = 3(S - 18)
2S - 18 = 3S - 54
2S - 3S = -54 + 18
-S = - 36
Where am I correct ?
2S - 18 = 3S - 54
2S - 3S = -54 + 18
-S = - 36
Where am I correct ?
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Mon May 09, 2016 4:01 pm
You ask....Where are you correct ?.......
2S - 18 = 3(S - 18) ......this is the equation I gave at the end of my last post equating the depth at the deep end to 3 times the depth at the shallow end after draining 18 inches.....OK
2S - 18 = 3S - 54 .....You have multiplied out the brackets on the RHS .......this is OK.
2S - 3S = -54 + 18 .....You have collected all the "S" terms to the LHS and all the numbers to the RHS....and you have signs changed for the terms that moved to the other side ....This is OK.
-S = - 36 ......You simplified each side (or worked out each side) .....this is OK.
Your problem now is probably you have found "-S" ......so how do you find "+S" or simply "S"
If you multiply a minus quantity by -1 you change its sign......so _S x -1 = +S or simply "S"
But what you do on one side of the equation you must do on the other to keep the equation balance.
So both sides need to be multiplied by -1.
That will give you a value for S
Then you have to use the relationship between D and S to fins the value for D
You should be able to do that......Its all in these last few posts... Have a go at doing it.
2S - 18 = 3(S - 18) ......this is the equation I gave at the end of my last post equating the depth at the deep end to 3 times the depth at the shallow end after draining 18 inches.....OK
2S - 18 = 3S - 54 .....You have multiplied out the brackets on the RHS .......this is OK.
2S - 3S = -54 + 18 .....You have collected all the "S" terms to the LHS and all the numbers to the RHS....and you have signs changed for the terms that moved to the other side ....This is OK.
-S = - 36 ......You simplified each side (or worked out each side) .....this is OK.
Your problem now is probably you have found "-S" ......so how do you find "+S" or simply "S"
If you multiply a minus quantity by -1 you change its sign......so _S x -1 = +S or simply "S"
But what you do on one side of the equation you must do on the other to keep the equation balance.
So both sides need to be multiplied by -1.
That will give you a value for S
Then you have to use the relationship between D and S to fins the value for D
You should be able to do that......Its all in these last few posts... Have a go at doing it.
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Mon May 09, 2016 5:35 pm
-S = - 36
-S * -1 = S
- 36 * -1 = 36
S = 36
D = 72 (Twice the shallow end).
-S * -1 = S
- 36 * -1 = 36
S = 36
D = 72 (Twice the shallow end).
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Mon May 09, 2016 6:25 pm
Yes, thats it now......matches the answers given with the question.....
It wasn't too hard a sum after all......
It wasn't too hard a sum after all......
- Guest
- Guest
Re: Original Depths: Deep and Shallow Parts
by Guest » Wed May 11, 2016 9:54 am
[tex]2x = y[/tex]
[tex]3(x - 18) = y - 18[/tex]
[tex]3x - 54 = 2x - 18[/tex]
[tex]x = 36[/tex]
[tex]y = 72[/tex]
[tex]3(x - 18) = y - 18[/tex]
[tex]3x - 54 = 2x - 18[/tex]
[tex]x = 36[/tex]
[tex]y = 72[/tex]
- Guest
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