Question

Patricia has $34,000 to invest. She invests some at 17% and the balance at 20%. Her total annual interest income is $6245. Find the amount invested at each rate.

Answer 1

Let x = amount invested at 17%, and y = amount at 20%.
Then
x + y = 34,000
0.17x + 0.20y = 6,245

Substitute y = 34,000 − x into the second equation:
0.17x + 0.20(34,000 − x) = 6,245
0.17x + 6,800 − 0.20x = 6,245
−0.03x = −555 → x = 18,500

y = 34,000 − 18,500 = 15,500

So Patricia invested $18,500 at 17% and $15,500 at 20%. (Check: 0.17·18,500 = 3,145; 0.20·15,500 = 3,100; total = 6,245.)