Question

Ask Your Teacher Equal amounts are invested at 2%, 7%, and 9% annual interest. If the three investments yield a total of $828 annual interest, find the total investment.

Answer 1

Answer:

$4600

Step-by-step explanation:

Write an equation to represent the problem.

Interest is calculated by multiplying the interest rate with the investment. Multiplying each of the rates (2%, 7% and 9%) in decimal form with the investment amount is equal to the annual interest, (828).

Convert a percentage to decimal form by dividing by 100:

2% ÷ 100 => 0.02

7% ÷ 100 => 0.07

9% ÷ 100 => 0.09

let "P" represent the amount of money for the total investment

0.02P + 0.07P + 0.09P = 828

Use the equation to solve for "P". Simplify by collecting like terms (numbers that have the same variable) then isolate "P" by moving the other numbers to the right side. To move a number to the other side, do it's reverse operation to both sides of the equation. (The reverse of multiplying is dividing).

0.02P + 0.07P + 0.09P = 828        Collect like terms

0.18P = 828        Isolate "P"

0.18P/0.18 = 828/0.18        Divide both sides by 0.18

P = 828/0.18         "P" is isolated because 0.18 cancelled out. Simplify.

P = 4600        Total investment

Therefore the total investment is $4600.