Problem A

Jack has $800 invested in two accounts. One pays 3% interest per year and the other pays 6% interest per year. The amount of yearly interest is the same as he would get if the entire $800 was invested at 5.25%. How much does he have invested at each rate?

Problem B

Jill has 800 L of acid solution. She obtained it by mixing some 3% acid with some 6% acid. Her final mixture of 800 L is 5.25% acid. How much of each of the 3% and 6% solutions did she use to obtain her final mixture?

In Problem A, let x represent the amount invested at 3% interest, and in Problem B, let y represent the amount of 3% acid used.

(a) Solve Problem A.
(b) Solve Problem B.
(c) Explain the similarities between the processes used in solving Problems A and B.