Question

A scientist has two solutions which she has labeled solution A and solution B. Each contains salt. She knows that solution A is 65% salt and solution B is 80% salt. She wants to obtain 90 ounces of a mixture that is 75% salt. How many ounces of cleave solution should she use?

Answer 1

Answer: Let's assume the scientist uses x ounces of solution A and y ounces of solution B to obtain 90 ounces of the mixture with 75% salt.

We need to set up a system of equations based on the given information:

The total amount of mixture: x + y = 90 ounces

The total amount of salt in the mixture: 0.65x + 0.80y = 0.75 * 90

Now, let's solve this system of equations to find the values of x and y:

From the first equation, we can express y in terms of x:

y = 90 - x

Now, substitute this value of y in the second equation:

0.65x + 0.80(90 - x) = 67.5

Now, solve for x:

0.65x + 72 - 0.80x = 67.5

-0.15x = -4.5

x = 30

Now that we have the value of x, we can find y:

y = 90 - x

y = 90 - 30

y = 60

So, the scientist should use 30 ounces of solution A and 60 ounces of solution B to obtain 90 ounces of the mixture with 75% salt.