Let the amount invested in the first account be x and let the amount invested in the second be 8000 - x We have PRT/100 where P is her principal and r, her rate and t, the time So in the first account I = x * 5 * 1/100 I = 5x/100 On the other hand if she gets 6% interest in the second account, we have I = PRT/100 So we have I = (8000 - x) * 6 * 1/ 100 I = (48000 - 6x)/100 But the combined interst is 438 so we have 5x/100 + (48, 000 - 6x)/100 = 438 Multiply through by 100 5x + 48, 000 - 6x = 43800 -x = 43800 - 48, 000 -x = -4200 Hence x = 4200. She will have to invest 8000 - 4200 in the second account which is 3800
Simple interest rate is given by: I=(PRT)/100 let the amount invested in 5% S.I. be $x and amount invested in 6% S.I. be $(8000-x) Interest obtained from 5% will be: I=5/100×1×x=0.05x
Interest obtained from 6% will be: I=6/100×1×(8000-x)=0.06(8000-x) therefore total interest earned from the to schemes will be: 0.05x+0.06(8000-x)=438 solving for x we obtain: 0.05x+480-0.06x=438 0.05x-0.06x=438-480 -0.01x=-42 x=-42/(-0.01) x=$4200 hence amount invested in 5% S.I. is $4200 and amount invested in 6% S.I. is (8000-4200)=$3800
