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) The sum of the two expressions in Exercise 66(a) must equal the total amount of interest earned in one year. Write an equation representing this fact.

Data from in Exercise 66(a)

(a) Write expressions that represent the amount of interest Jack earns per year at 3% and at 6%.

(b) The sum of the two expressions in Exercise 66(b) must equal the amount of pure acid in the final mixture. Write an equation representing this fact.

Data from in Exercise 66(b)

(b) Write expressions that represent the amount of pure acid in Jill’s 3% and 6%  acid solutions.