Length - Parts

[Guest]

A fishing rod consists of two parts - upper and lower.

The length of the upper part is to the lower part as 5 to 7, and 9 times the upper part together with 13 times the lower part exceeds 11 times the total rod by 36 inches. Calculate length of the two parts.

Let U = upper part.
Let L = lower part.
Let T = total rod.

My attempt:
The length of the upper part is to the lower part as 5 to 7 - Don't understand statement.
9U + 13L + 11L - T - 36

How do I proceed from this point ?

[Guest]

"A fishing rod consists of two parts - upper and lower"
T = U + L

"The length of the upper part is to the lower part as 5 to 7"
This is talking about the ratio of lengths U:L = 5:7, or put in a more useful form
U/L = 5/7

"9 times the upper part together with 13 times the lower part exceeds 11 times the total rod by 36 inches."
9U + 13L - 11T = 36

Hope this helps,

R. Baber.

[Guest]

That helped. Now, how do I find the length of each part ?

[Guest]

T=U+L can be rewritten as U+L-T = 0
U/L = 5/7 can be rewritten as U = (5/7)L which can be rewritten as 7U = 5L or 7U-5L = 0
Putting these together with the last equation gives:

U+L-T = 0
7U-5L = 0
9U+13L-11T = 36

You have three linear equations in three unknowns, there are lots of tutorials out there that will walk you through on how to solve this, for example
https://www.youtube.com/watch?v=cS_Sk-UaBg4

Hope this helped,

R. Baber.

[Guest]

"T=U+L can be rewritten as U+L-T = 0
U/L = 5/7 can be rewritten as U = (5/7)L which can be rewritten as 7U = 5L or 7U-5L = 0"

I don't understand these.

[Guest]

"U+L-T = 0
7U-5L = 0
9U+13L-11T = 36"

17U + 9L -12T = 36 I tried to add.

How do I proceed ?

I viewed several videos but I am still confused.

[Guest]

Starting with T=U+L
swap the left hand side and right hand side to get
U+L = T
Subtract T from both sides to get
U+L-T = T-T
The right hand side simplifies to 0, so
U+L-T = 0

Starting with U/L = 5/7
Multiply both sides by L
to get (U/L)L = (5/7)L
The left hand side can be simplified as dividing by L then multiplying by L is the same as doing nothing, so we get
U = (5/7)L = (5L)/7
Multiply both sides by 7 to get
7U = 5L
subtract 5L from both sides to get
7U-5L = 0

I rewrote the equations in this form to make it more obvious that you have three linear equations in three unknowns.


Just adding the equations up won't solve the equations. I suggest you google solving "simultaneous equations" there will be lots of examples online showing you how to find the answer when you have 2 equations in 2 variables. In general there are two methods that you will come across:

1) The elimination method:
Here you multiply the equations by some factor (which you have to figure out yourself) then add or subtract the equations.
If you choose the factors carefully when you add (or subtract) the equations one of the unknown variables will cancel itself out and you will be left with one equation in one unknown variable which is easy to solve. You can then substitute the value back into the equations to work out the other variable.

2) The substitution method:
Here you take one of the equations and try to rewrite it so that you have a formula for one of the variables in terms of the other (e.g. you can rewrite 2x+3y= 1 as x = (1-3y)/2). Then you substitute this into the other equation to get one equation in one unknown variable, which is easy to solve. You then substitute the value back into the equations to work out the remaining unknown (just like in the elimination method).

I suggest you go online and do lots of examples and familiarise yourself with these two tricks for solving simultaneous equations. Once you do that it should be easier to grasp how you can use these same tricks to solve 3 simultaneous equations in 3 variables.

It's the same idea: Using the elimination method you can multiply the first and second equation by some factor so that when you combine them you get rid of one of the variables, next take the first and third equations and try to eliminate the same variable, you should now have two equations in two unknowns which you should know how to solve. Or alternatively you can solve things using the substitution method: first rewrite the first equation so that one of the variables is expressed in terms of the other two variables then substitute this into the second and third equations, you should now have two equations in two unknowns which you should know how to solve.

Unfortunately if you are not comfortable solving simultaneous equations in 2 variables then doing it for 3 variables will just completely confuse you. I can give you the answer but then you'll learn nothing. You have to go away and look up tutorials on 2 variable simultaneous equations, practise them a lot, then look at tutorials on 3 variable simultaneous equations. Also it might not be such a bad idea to refresh your knowledge on how to rearrange equations, as you seem to be struggling with that too. Don't give up, keep trying and keep practising and you'll get there. If you get stuck on understanding how these methods work ask on this forum or other forums, people are more likely to help you out in understanding how a method works (especially if you demonstrate that you've been trying and putting in some effort (explain what you think is going on, and where you are confused)), they are less likely to just do your homework questions for you, as that doesn't really help anyone.

Hope this helped,

R. Baber.

[Guest]

That helped. Not homework question. I have been out of school nearly 40 years and am trying to relearn math/algebra on my own. I was just needing some assistance.

[Guest]

Good for you. Out of interest, are you relearning for a particular purpose, or just learning for the sake of learning?

R. Baber.

[Guest]

Just for the sake of learning. Thanks.