Answer:
$20,000 into the account earning 3% interest
$3000 into the account earning 7% interest
Step-by-step explanation:
let "a" be the account that earns 3% annual simple interest
let "b" be the account that earns 7% annual simple interest
Create two equations to represent the total investment and interest:
a + b = 23,000
0.03a + 0.07b = 810
When two or more equations have the same variables, it is called a "system" and you can solve for the variables.
Solve using the method substitution.
Rearrange one of the equation so that one variable is isolated
a + b = 23,000
a = 23,000 - b
Substitute "a" for 23,000 - b in the other equation
0.03a + 0.07b = 810
0.03(23,000 - b) + 0.07b = 810 Distribute over the bracket
690 - 0.03b + 0.07b = 810 Combine like terms (with the variable "b")
690 + 0.04b = 810 Start isolating "b" by subtracting 690 on both sides
0.04b = 120 Divide both sides by 0.04
b = 3000 Investment in 7% interest account
Substitute "b" for 3000 in the simpler equation to find "a"
a + b = 23,000
a + 3000 = 23,000 Subtract 3000 from both sides to isolate "a"
a = 20,000 Investment in 3% interest account
Therefore Larry Mitchell invested $20,000 into the account earning 3% annual simple interest and $3000 into the account earning 7% annual simple interest.
