What is the amount invested for each rate?

Question

A person invested $7500 for 1 year, part at 8% part at 10% and the remainder at 13%. The total annual income from these investments was $839. The amount of money invested at 13% was $300 more than the amounts invested at 8% and 10% combined. Find the amount invested at each rate.

 

The person invested$____ at 8%,$___ at 10% and $___ at 13%

Answer 1

Hi Amanda,

 

Let x = amount at 8%

Let y = amount at 10%

 

(x + y +300) = amount at 13%  (300 more that the amounts at 8% and 10% combined

 

839 = .08*x + .1y + .13(x + y +300)

 

7500 = x + y + (x+y+300)

 

now lets simplify each equation

 

839 = .21x + .23y + 39

 

7200 = 2x + 2y

 

Lets get rid of the decimals in the first equation - we will mutliply by 100

 

83900 = 21x + 23y +3900

 

80000 = 21x + 23y

 

and now lets multipy each equation by a number that will make of the the terms the same so we can get rid of it

 

160000 = 42x + 46y           (multiplied equation by 2

 

151200 = 42x + 42y            (multiplied by 21

 

now subtract to solve for y

 

8800 = 4y

 

y = 2200              (amount at 10%

 

now find x

 

7200 = 2x + 2y

 

7200 = 2x + 4400

 

2800 = 2x

 

x = 1400              (amount at 8%

 

x + y + 300

 

1400 + 2200 + 300 = 3900         (amount at 13%

 

 

now you can check it

 

 

1400(.08) + 2200(.1) + 3900(.13)

 

112 + 220 + 507

 

= 839 and it all checks out

 

Hope this helps