Mixture Word Problem

Question

How much fresh water should be mixed to a 30% salt water solution, to obtain 90 gallons of a 23% salt water solution?

Answer 1

Let x = amount of fresh water

 

Then, 90-x = amount of 30% solution

 

Then, salt content of fresh water = 0% of x = 0x = 0

 

salt content of 30% solution = 30% of 90-x = 0.30(90-x)

 

salt content of mixture = 23% of 90 = 0.23(90)

 

So, 0 + 0.30(90-x) = 20.70

 

            27 - 0.30x = 20.70

 

                  -0.30x = -6.30

 

                         x = 21 gallons of water

 

             

Answer 2

Abigail,

 

Let x be the number of gallons of fresh water (no salt) and y be the number of gallons of 30% salt water.

 

This means that all the salt in the final solution comes from the original 30% solution.  So, let's find the total amount of salt in the final solution:

 

Salt content in final = 90 * .23 = 20.7 gallons

 

Now, since all  salt comes from the 30% solution, we can find the number of gallons of 30% this way:

 

.3y = 20.7 (since 30% of the original solution is salt)

 

y = 69 gallons in the original 30% solution.

 

We also know that the sum of the gallons of fresh water and 30% solution is 90.

 

x + y = 90

 

x + 69 = 90

 

x = 21 gallons of fresh water need to be added.