I cannot answer, please help?

Question

Last year Felipe had $20,000 to invest. He invested some of it in an account that paid 5% 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 $1020 in interest. How much did he invest in each amount?

Answer 1

The simple interest equation is I = Prt where P is your principal investment, r is your interest rate as a decimal, and t is time.

To answer this question we need to set up a system of equations.

For account 1 lets let x represent P and for account 2 lets let y represent P.

20000 = x + y represents how much money was invested

For the two accounts I = x(.05)(1) and I = y(.07)(1) so

1020 = .05x + .07y represents how much interest was made

Solve the system either through elimination or substitution

elimination:

1020 = .05x + .07y

(-.05)20000 = (-.05)x + (-.05)y

-1000 = -.05x - .05y

+ 1020 = .05x + .07y

20 = .02y

y = 1000

substitution:

1020 = .05x + .07y

x = 20000 - y

1020 = .05(20000 - y) + .07y

1020 = 1000 + .02y

20 = .02y

y =1000

Plug y back into one of your original equations to solve for x.

x = 20000 - 1000

x =19000

Check your answer by plugging in the principal values (x and y) into your interest equation

1020 = .05x + .07y

1020 = .05(19000) + .07(1000)

1020 = 950 + 70

1020 = 1020