2 equations 2 unknowns

Question

$30000 invested into 2 accounts, one account has 5% simple interest peryear, the rest of teh money goes into another account that has 8% interest per year after one year she receices $2160 in interest, how much did she invest into each account

Answer 1

.05(x) + .08(30000-x) = 2160

.05x -.08x = 2160 -.08(30,000)

.03x = .08(30,000)-2160

.03x = 8(300)-2160 = 2400-2160 = 240

x = 240/.03 = 24000/3 = $8000 invested at 5%

30000-x = 30,000-800= $22,000 invested at 8%

30,000 earning 2160 interest means an average return of 2160/30000 = 216/3000=72/1000

= 7.2/100 = 7.2% interest rate

7.2 is much closer to 8 and to 5, so most of the money is invested at 8%

8 is within .8 of 7.2, 5 is within 2.2 of 7.2

.8/2.2 = 8/22 = 4/11

4/11 = 8000/22000 = 8/22 = 4/11

11 times