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Q: Mike invested $7000 for one year. He invested part of it at 8% and the rest at 12%. At the end of the year he earned $764 in interest. How much did he invest at each rate?
x = amount of money Mike invests at 8%
y = amount of money Mike invests at 12%
Since "Mike invested $7000 for one year.", this means that
Also, because "He invested part of it at 8% and the rest at 12%. At the end of the year he earned $764 in interest.", this translates to
. Multiplying every term by 100 gets us
So we have the system of equations:
Let's solve this system by substitution
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
Start with the first equation
from both sides
Rearrange the equation
, we can now replace each
in the second equation with
to solve for
into the second equation. In other words, replace each
. Notice we've eliminated the
variables. So we now have a simple equation with one unknown.
Combine like terms on the left side
Subtract 84000 from both sides
Combine like terms on the right side
Divide both sides by -4 to isolate x
So this means that Mike invested $1,900 at 8%
Since we know that
we can plug it into the equation
(remember we previously solved for
in the first equation).
Start with the equation where
was previously isolated.
Combine like terms
So Mike invested $5,100 at 12%
So Mike invested $1,900 at 8% and $5,100 at 12%