Algebra Question

Question

Manuela has saved $12000 over the last 10 years. She decides to invest some of it at 5.5% annual interest and the rest at 4.5% annual interest. After one year, her total interest from both accounts is $628. How much did she invest in each account?

A. Define Variables to represent the unknowns and setup the necessary equations to answer the question.

B. Algebraically solve the equation you created and express your final answer using a complete sentence and appropriate units.

Answer 1

Hi Marley M.

Manuela invested $8800 at 5.5% and $3200 at 4.5%.

A system of equations solving with substitution were used to determine the amounts invested

Equation 1 for Total amount invested

Let x = amount invested at 5.5%

Let y = amount invested at 4.5%

x + y = 12000

So y = 12000 - x

Equation 2 to Total amount of interest earned over 1 year

0.055x + 0.045y = 628

Since from Equation 1 we know y = 12000 - x we can make this substitution into Equation 2 and solve for x

0.055x + 0.045(12000 - x) = 628

Multilply through the parentheses

0.055x + 540 - 0.045x = 628

Combine like terms

0.055x - 0.045x + 540 = 628

0.01x + 540 = 628

Subtract 540 from both sides of the equation

0.01x = 88

Divide both sides of the equation by 0.01

x = 88/0.01

x = 8800

Since y = 12000 - x = 12000- 8800 = 3200

y = 3200

Checking

Equation 1

x + y = 12000

8800 + 3200 = 12000

Equation 2

0.055x + 0.045y = 628

0.055(8800) + 0.045(3200) = 628

484 + 144 = 628

628 = 628

I hope this helps please send me a message if you have any questions