Solving a tax rate or interest rate problem using a system of linear equations

Question

Last year, Felipe had $10,000 to invest. He invested some of it in an account that paid 8%

simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $790 in interest.

How much did he invest in each account?

First account:

Second account:

Answer 1

Hi Kristen N

9000 was invested at 8%

1000 was invested at 7%

Let x = the portion invested at 8%

Let y = the portion invested at 7%

Total Principal = 10000

x + y = 10000

And.

y = 10000 - x

Intertest earned = 790

08x + .07(10000 - x) = 790

Multiply through

.08x + 700 - .07x = 790

Combine like terms

.01x + 700 = 790

Subtract 700 from both sides if the equation

.01x = 790 - 700

.01x = 90

Divide both sides by .01

x = 9000

y = 10000 - 9000 = 1000

Checking

.08(9000) + .07(1000) = 790

720 + 70 = 790

I hope this helps

Answer 2

We find simple interest using the equation A = A₀(1 + rt) where "A" is the amount of money you have at time "t" in years, A0 is the initial amount of money (at time t = 0), and "r" is the annual interest rate.

So, in this case:

Let's let "x" be the amount he invested in the first account (8% interest account) and let's let "y" be the amount of interest he earned in the 8% account.

So the total amount he had at the end was x + y and (which equates to the "A" in the equation so:

x + y = x(1 + (0.08)(1))

x + y = 1.08x

y = 0.08x

For the other account, he invested "10,000 - x" and he earned "790 - y" so:

(10000 - x) + (790 - y) = (10000 - x)(1 + (0.07)(1))

10790 - x - y = (10000 - x)(1.07)

10790 - x - y = 10700 - 1.07x

90 + 0.07x = y

So our two equations are:

y = 0.08x

y = 90 + 0.07x

We can solve by setting them equal to each other:

0.08x = 90 + 0.07x

0.01x = 90

x = 90/0.01 = 9000

So $9000 was invested in the first account (8% account) and $1000 was invested in the second account (7% account)