sherry invested a sum of money at 6% and invested a second sum that was $1,500 greater than the first sum, at 5%. if the total annual income was $570, how much was invested at each rate?

Answer 1

.Sherry invested x amount of money at 6%, and $1,500 more at 5%, earning interest for the year of $570

$570 annual interest is the sum of interest earned at 6% (.06x) plus interest earned at 5% ( (.05)(x+$1,500))

5% = .05, 6% = .06

.06x + .05(x+$1,500) = $570 where x=amount invested at 6%, x+1500 = amount invested at 5%

$570 = the total interest earned on both investments

.06x + .05x + .05(1,500) = 570

.06x + .05x = 570 - .05(1,500)

(.06 + .05)x= 570 - 75

.11x = 495

x = 495/.11

= 4,500

x = $4,500 invested at 6%

x+$1500 = $6,000 invested at 5%

check the answers:

.06($4500) + .05($6000) = $270 + $300 = $570

or alternatively,

you could have solved it as x-1500 = amount invested at 6%, x = amount invested at 5%

.06(x-1500) + .05x = 570

.06x + .05x = 570 +90 = 660

x = 660/(.11) = $6,000 invested at 5%

x-1500 = 6000-1500 = $4500 invested at 6%

570/(4500+6000) = 570/10500) = about 5.43% average interest

if the same amount had been invested at both 5% and 6%, average interest would have been exactly 5.5%

but

since more is invested at 5% than 6%, the average will be closer to 5% than 6%. 5.43% is slightly closer to 5% than to 6%

the general method is similar to calculating your GPA, your courses' grade point average.

If you had 45 grades of 60 each and 60 grades of 50 each your GPA would be a weighted average

45(60) + 60(50) = about 105(54.3) Your GPA = 54.3

2700 + 3000 = 5700 = about 54.3(45+60)