How do you do this math word problem? ?

Question

If you have $8000 to invest for college and you are investing part at 7% interest and part at 5% interest, how much should you invest at each rate in order to get $500 in interest after one year?

and please show your work so that i understand how you got the answer

thank you! :)

Answer 1

5%*x + 7%*($8000 - x) = $500; where x is the amount invested at 5% and what's left of the $8000 is invested at 7%.

0.05x + 0.07($8000 - x) = $500

0.05x + $560 - 0.07x = $500

-0.02x = -$60, or 0.02x = $60

x = $3000

Invest $3000 at 5% and $5000 at 7%.

Answer 2

We're looking for two amounts that will equal $8000.

x = first amount

(8000 - x) = second amount

The combined interest on both amounts has to equal $500. Multiply the interest rates (7% and 5%) by the two amounts.

0.07 times x = interest on first amount.

0.05 times (8000 - x) = interest on second amount.

Then make an equation out of it.

((0.07 (x)) + ((0.05 (8000 - x)) = 500

And solve.

0.07x + 400 - 0.05x = 500

0.02x + 400 = 500

0.02x = 100

x = 5000

8000 - x = 3000

Answer 3

We should first introduce two variables (as always x and y) standing for each separated amount of money.

We know that sum of x and y will be $8000

x+Y=8000

it is our first equation and cause we have two variables we need two.  The second one is that

0.07X+0.05Y=500

the first equation can be rewrite as this  

x=8000-Y

and in the second equation we can replace all x’s with 8000-b and the second equation will be

0.07*8000-0.07Y+0.05Y=500

if you want your work to be easier multiply two sides by

100 and it will be

56000-2y=50000

and  

2y=6000

so

y=3000

and

x=5000

i hope you'v understand it  

Answer 4

let money invested at 7% interest be $P

money invested at 5% will be $8000-$P

A.T.P

{(P*7*1)/100} + {(8000-P*5*1)/100} = $500

or,(7P+40000-5P)/100 = $500

or,2P+40000 = $50000

or,2P = $10000

or,P = $5000

money invested at 7% is $P = $5000

&

money invested at 5% is $8000-$P =$8000-$5000 = $3000