Question

A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $540?

Answer 1

The amount invested at

Explanation:

The total amount invested is $5000

Let x be the investment at 5%

Let y be the investment at 15%

Mathematically, this can be expressed as

x + y = 5000 -- equation 1

Since the first part of the investment is invested at 5% and the second part is at 15%

0.05x + 0.15y = 540 --------- equation 2

The systems of equations can be solved simultaneously using the substitution method

x + y =5000 ----- equation 1

0.05x + 0.15y = 540 ------ equation 2

Isolate x in equation 1

x = 5000 - y

Substitute the value of x into equation 2

0.05(5000 - y) + 0.15y = 540

Open the parenthesis

250 - 0.05y + 0.15y = 540

Collect the like terms

-0.05y + 0.15y = 540 - 250

0.1y = 290

Divide both sides by 0.1

0.1y/0.1 =290/0.1

y = $2900

Recall that equation 1 is

x + y = 5000

y = $2900

x = 5000 - y

x = 5000 - 2900

x = $ 2100

Hence, the investment at 5% is $2100 and the investment at 15% is $2900