Abigail R.

asked • 08/04/16# Mixture Word Problem

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

More

## 2 Answers By Expert Tutors

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

Richard C. answered • 08/04/16

Tutor

5
(60)
Yes, You Can Learn Math!

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.

## Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

Norbert W.

08/04/16