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Question

Christy invests $2200 in one account and $2400 in an account paying 3 % higher interest. At the end of one year she had earned $532 in interest. At what rates did she invest?

Answer 1

Let's invest $2200 at rate x% or x/100

Then invest $2400 at (x+3)% or (x+3)/100

 

Assuming our interest is compounded annually:

 

I = prt

Interest = principal(rate)(time).  Total interest earned will be the sum of

the interest earned at the two rates:

532 = 2200(x/100)(1) + 2400[(x+3)/100](1)

53200 = 2200x + 2400(x+3)

factor out 200

266 = 11x + 12(x+3)

266 = 11x + 12x + 36

230 = 23x

10 = x

 

She invested $2200 at 10%

She invested $2400 at 13%

 

Check:  532 = 2200(10/100) + 2400(13/100)

            532 = 220 + 312

            532 = 532

            This checks as correct