. 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?

Question

campbell_st · Answer

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