How many ounces of each solution should she use?

Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 35% salt and Solution is 60% salt. She wants to obtain 110 ounces of a mixture that is 55% salt. How many ounces of each solution should she use?

Answer 1

A + B = 110 (scientist wants to end up with 110 ounces)

Now write an equation involving salt: salt in A + salt in B = salt in mixture

.35A + .6B = .55(110)

I suggest multiplying the 2nd equation by 100 to clear the decimals.

35A + 60B = 6050

Since it is easy to solve the 1st equation for A (or B) probably the substitution method is easiest.

From the 1st equation: A = 110-B. Substitute that into the 2nd equation:

35(110-B) + 60B = 6050

3850-35B +60B = 6050

25B = 2200

B = 88

A = 110-88=22

Check:

.35(22) + .6(88) =? .55(110)