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

Algebra ->  Finance -> 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       Log On


   

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) About Me  (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 x%2By=600. Basically all the parts must add up to the whole. Solve for y to get y=600-x


"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 0.08x%2B0.12y=56. 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 8x%2B12y=5600



8x%2B12y=5600 Start with the given equation.


8x%2B12%28600-x%29=5600 Plug in y=600-x (ie replace EVERY y with '600-x')


8x%2B7200-12x=5600 Distribute.


-4x%2B7200=5600 Combine like terms on the left side.


-4x=5600-7200 Subtract 7200 from both sides.


-4x=-1600 Combine like terms on the right side.


x=%28-1600%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=400 Reduce.


y=600-x Go back to the equation with an isolated y


y=600-400 Plug in x=400


y=200 Subtract


So the solutions are x=400 and y=200


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