A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 30% salt and Solution B is 70% salt. She wants to obtain 120 ounces of a mixture that is 65% salt. How many ounces of each solution should she use?

Solution A: 15 ounces

Solution B: 105 ounces

Step-by-step explanation:

A + B = 120

A = 120 - B

0.3A + 0.7B = 0.65 (120)

0.3A + 0.7B = 78

0.3 (120 - B) + 0.7B = 78

36 - 0.3B + 0.7B = 78

0.4B = 42

B = 105

A = 120 - 105

A = 15

15 ounces solution A

105 ounces solution B

Step-by-step explanation:

Let x be the amount of solution A

We need a total of 120 ounces of solution

Therefore we need

120-x ounces of solution B

Take the ounces of solution A times the percentage salt + the ounces of solution B times the percentage salt and this should equal the total ounces time the percentage sale

.3 x + (120-x) *.7 = 120 *.65

Distribute

.3x + 84 -.7x = 78

Combine like terms

-.4x = - 6

Divide each side by -.4

-.4x/-.4 = - 6/-.4

x = 15

We need 15 ounce of solution A

We need 120 ounces total

120-15 = 105 ounces of solution B