SOLUTION: The question is: Tina invested $600, part at 8% interest per year, and the rest at 12% interest per year. At the end of a year, the total interest was $56. How much did she invest

Question 467383: The question is: Tina invested $600, part at 8% interest per year, and the rest at 12% interest per year. At the end of a year, the total interest was $56. How much did she invest at each rate?
I tried setting up an equation as (0.08)x+(.12)y=56. X and Y being the quantities that were invested in either stock. Although I think I can get an answer from doing the substitution method, it would be incredibly tedious, and the division would be very annoying. Please explain how to do this problem, and what equation should be set up.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = amount invested at 8%, y = amount invested at 12%

"Tina invested $600" means . Basically all the parts must add up to the whole. Solve for y to get

"part at 8% interest per year, and the rest at 12% interest per year. At the end of a year, the total interest was $56" means that . Multiply EVERY term by 100 to change 0.08 to 8, change 0.12 to 12 and change 56 to 5600 (doing all this makes every number a whole number; this is entirely optional, but I find it helps). So the new equation is now

Start with the given equation.

Plug in (ie replace EVERY y with '600-x')

Distribute.

Combine like terms on the left side.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

Go back to the equation with an isolated y

Plug in

Subtract

So the solutions are and

So she invested $400 at 8% and $200 at 12%

RELATED QUESTIONS
Bob invested $24000. He invested part of it at 8% interest per year and the rest at 10%... (answered by richwmiller,greenestamps)

Bethany invested $2500, part at 8% per year and the rest at 12% interest per year. In one (answered by stanbon)

A total of $2000 was invested: part at 8% and the rest at 12% per year. If after one... (answered by macston)

Deshi invested $32,000. He invested part of it at 8% interest per year and the rest at... (answered by mananth)

A principal of $2500 is invested; part at 8% per annum and the rest at 12% per annum. In... (answered by checkley71)

# 9. Mike invested $7000 for one year. He invested part of it at 8% and the rest at 12%. (answered by jim_thompson5910)

Mike invested $7000 for one year. He invested part of it at 8% and the rest at 12%. At... (answered by checkley75)

John invested $7000 for one year. He invested part of it at 8% and the rest at 12%. At... (answered by Mathtut)

Kevin invested $7000 for one year. He invested part of it at 8% and the rest at 12%. At... (answered by Mathtut)