Question

A scientist mixes water (containing no salt) with a solution that contains 30% salt. She wants to obtain 120 ounces of a mixture that is 20% salt. How many ounces of water and how many ounces of the 30% salt solution should she use?

Answer 1

She should use 40 ounces of water and 80 ounces of 30% salt solution.

Step-by-step explanation:

Let's call x the number of ounces of water and y the number of ounces of the 30% salt solution.

She wants to obtain 120 ounces of the mixture, so

x + y = 120

Addition she want that the mixture to be 20% salt, it means that

0x + 0.3y = 0.2(120)

0.3y = 24

Because the water has no salt, the 30% salt solution has 30% of salt and the total mixture is 120 ounces.

Now, we can solve the second equation for y, so

0.3y = 24

0.3y/0.3 = 24/0.3

y = 80

Then, using the first equation, we can find x, so

x + y = 120

x + 80 = 120

x + 80 - 80 = 120 - 80

x = 40

Therefore, she should use 40 ounces of water and 80 ounces of 30% salt solution.