Question

. Select the set of equations that represents the following situation: Mary invested one amount at 7% simple interest, and a second amount at 5% interest, earning $29.80 in one year. If she had switched the amounts, she would have earned $35.00. What were the two amounts?

Answer 1

let x = amount 1 and y = amount 2

using I = Prn

then the equations are..... 7% = 0.07 5% = 0.05 n = 1

0.07x + 0.05y = 29.80 (1)
0.05x + 0 07y = 35.00 (2)

solve by elimination
multiply equation (1) by 5 and subtract equation (2) multiplied by 7

0.35x + 0.25y = 149
- 0.35x + 0.49y = 245
------------------------
-0.24y = -96

y = $400

substitute into equation (1) to find x

0.07x + 0.05(400) = 29.80

0.07x = 9.80

x = $140

the investments where y = $400 and x = $140