Mandy invests $800...?

Question

If you could show work it would be awesome, I can't remember how to do these...

Mandy invests $800. She invests part of it a fund that pays 9% per annum and the rest in a fund that pays 5% per annum. After one year, she had earned $54 interest. How much did she invest in each fund?

Answer 1

let x= the amount in the fund paying 9%
let y= the amount in the fund paying 5%

x+y=800
y=800-x

0.09x+0.05y=54
0.09x+0.05(800-x)=54
0.09x+40-0.05x=54
0.04x=54-40
x=350

therefore she depositied $350 into the fund that pays 9% interest

y=800-x
=800-350
=450

and she depositied $450 into the fund that pays 5% interest.

Answer 2

OK

.09 x + .05 y = 54
x + y = 800 ; multiply top by 20

1.8x + y = 1080
x + y = 800 ; subtract bottom from top

.8x = 280
x = 350

So 350 was invested at 9%. 800-350 = 450 was invested at 5%

Check

.09(350) + .05(450) = 54??
31.50 + 22.50 =54??
54 = 54! YES!

Hope that helps.

Answer 3

.09x + .05(800-x) = 54 ==>
.09x + 40 - .05x = 54 ==>
.04x = 14 ==>
x= 350 (amount invested at 9%)
800-350 = 450 (amount in 5%)

check:
.09*350 = 31.50
.05*450 = 22.50
22.5 + 31.5 = 54

Answer 4

x is money at 9% and (800-x) is money at 5%
so (remember 9% as a decimal is .09)

.09(x) + .05(800-x) = 54
solve this
.09x + 40 - .05x = 54
.04x + 40 = 54
.04x = 14
x = 14/.04 = 350dollars at 9%
(800-x) = (800-350) = 450dollars at 5%

Answer 5

If she invested x in 9%, then she put 800-x in 5%,
.09x + .05(800-x) = 54
Solve for x,
x = $350
800-x = $450

Answer 6

let x be the amount invested in for 5%
then (800-x) is the amount invested for 9%

eq. 0.05x + 0.09(800-x) = 54
5x +9(800-x) = 5400
4x = 1800
x = 450

450 for 5% and 350 for 9%