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 150 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?

Answer 1

Let x be the number of ounces of solution a and y be the number of ounces of solution b.

We know that the total amount of mixture needed is 150 ounces, so we can write:
x + y = 150

To achieve a 70% salt mixture, we can write the equation:
0.65x + 0.8y = 0.7(150)

To solve for x and y, we can use substitution or elimination. Let's use substitution to solve for x.

From the first equation, we have:
x = 150 - y

Substituting this into the second equation:
0.65(150 - y) + 0.8y = 105

Simplifying:
97.5 - 0.65y + 0.8y = 105
0.15y = 7.5
y = 50

Now that we know y, we can find x using either of the original equations:
x + y = 150
x + 50 = 150
x = 100

Therefore, the scientist should use 100 ounces of solution a and 50 ounces of solution b to obtain 150 ounces of a mixture that is 70% salt.