alegreba help

Question

peter wants to invest enough money at 4.5% and 7.5% to earn $840. how much of his $15000 should he invest at each rate?

Answer 1

I am assuming the problem means that You get 4.5% and 7.5% of whatever you invest in a lump sum (not simple or compound interest over a period of time)

 

1. Define the variables

Let x = amount of money invested in the 4.5% return

Let y = amount of money invested in the 7.5% return

 

2. Set up Equations

x + y = 15000 because Peter is investing $150000 total

0.045x + 0.075y = 840 because Peter wants to earn exactly $840

 

3. Solve the System of Equations

Leave one variable on one side for the first equation

x = 15000 - y

 

Substitute x in the second equation with the 15000 - y

0.045(15000 - y) + 0.075y = 840

 

Solve for y

675 - 0.045y + 0.075 y = 840

0.03 y = 165

y = 5500

 

Substitute the y value back into the first equation to solve for x

x + y = 15000

x + 5500 = 15000

x = 9500

 

4. Substitute the x and y values back into the equations to verify the answer