Mixture - Percent

[Guest]

Seventy five lbs. of salt water contains 4% salt. 45 lbs. of fresh water is added. In the final solution, determine percent of salt.

My partial solution:

75 lbs. of salt water is 4% salt: 96% of the water is fresh (72 lbs.)

72 + 45 = 117 lbs. of fresh water in final solution.

How do I proceed ?

[Guest]

You just keep going......
you have found out there is 117 lbs total of fresh water in final solution
and you found there was 72 lbs fresh water in initial solution so if 75 lbs water+salt in initial solution, that means 3 lbs of salt in initial.
the 3 lbs of salt is still there......so add the final water and salt to get final lbs and work out percent.

[Guest]

117 lbs. fresh water in final solution + 3 lbs. salt in final solution = 120 lbs. salt water.

3 lbs. salt / 120 lbs. water = 0.025 = 2.5 % salt.

[Guest]

yes ok

[Guest]

Thanks. Would you please show how to solve algebraically ?

[Guest]

Generally with algebra let the unknown you are trying to find = "X" or some other letter
Then try and get an equation from the information given in the question
Here we have a known amount of salt and water solution and we add a known quantity of water and we want to find the percent of salt in the final solution. The unknown X is the final percent of salt.

The quantity of salt before = the quantity of salt after......only pure water is added.

0.04 x 75 = X(75 + 45)

3 = 120 x X

X = 3/120 = 1/40 = 0.025 = 2.5% salt

[Guest]

Thanks.

[Guest]

0.04 x 75 = x(75 + 45)

A question:

How would this formula be entered in a spreadsheet ? Just curious.

[Guest]

What we ended up with was an equation balancing the salt before and the salt after.

0.04 x 75 = X(75 + 45)
You have a calculation to do on the LHS and a calculation to do on the RHS
Normally you would do this on your calculator in stages and end up with..... 3 = 120X ...so X = 3/120 etc
OR re-arrange to get the unknown X on one side ..... X = (0.04 x 75)/(75+45) and do this on you calculator and you would end up with the same 3/120 = 1/40 = 2.5%

You could do the same calculations on a spreadsheet by putting the the re-arranged calculations in cells.....

In A2 put in as a heading...... Final Percent Salt
In A3 below it put in.......... =(0.04 x 75)/(75+45)x100
Multiply by 100 so as to display answer as percent OR format cell %
Don't forget the = sign at start of all formulas.
That will give the answer in one operation.

If you want a table as was the last question showing the percentage salt for each row against each lb of water added.....

In cell A1 put heading "lbs water added" and in B1 put heading " Percent Salt"
Fill series down column A from A2 down with the numbers 1 to 50 say....
In B2 put in the formula.... =(0.04 x 75)/(75+A2)x100
Copy this formula down column B alongside the numbers you filled in A
The reference "A2" in the formula will change automatically to "A3" then "A4" etc in each row as it is copied down.
So the formula will work out the percent for each row corresponding to the number in the cell in the A column.
When you come to the row with 45 lbs added you should see 2.5% in column B on that row.

[Guest]

Thanks.

[Guest]

Worked on the first try. Thanks again.

[Guest]

Percentage Calculation Formula,
x = (percent value /100)* Number

For Example,
What is 20% of 250?
x = (20/100)*250
x= 50
(or)

[Guest]

Thanks.