You can
put this solution on YOUR website!Let T represent the amount of money invested at 20%.
.
Let S represent the amount of money invested at 17%
.
From the problem, we can tell that T + S must equal the total investment of $21,000.
In equation form we can write this as:
.
T + S = 21000
.
This is one equation we can use.
.
Next we know that the amount of interest on T is 20% of T or 0.2*T. We also know that the
amount of interest on S is 17% of S or 0.17*S. If we add these two amounts of interest
we get the total interest of $3780. In equation form this is:
.
0.2*T + 0.17*S = 3780
.
This is the second equation we can use.
.
The problem asks us to solve for T, the amount of money invested at 20%. Suppose we return
to the first equation and solve it for S in terms of T.
.
The first equation is T + S = 21000. Let's subtract T from both sides of the equation and
when we do, we get that S = 21000 - T.
.
Next return to the second equation and for S in that equation let's substitute its equivalent,
21000 - T.
.
With that substitution, the second equation becomes:
.
0.2*T + 0.17*(21000 - T) = 3780
.
Do the distributed multiplication on the left side by multiplying 0.17 times each of
the terms in the parentheses. When you do that you get:
.
0.2*T + 3570 - 0.17T = 3780
.
If you combine the two terms that contain T by subtracting 0.17 from 0.2 the equation
becomes:
.
0.03*T + 3570 = 3780
.
Next, get rid of the 3570 on the left side by subtracting 3570 from both sides. After this
subtraction, the resulting equation is:
.
0.03*T = 210
.
Solve for T by dividing both sides of this equation by 0.03. When you do that, the equation
becomes:
.
T = 210/0.03 = 7000
.
So the answer is that $7,000 is invested at 20% and therefore the remaining $14,000 is
invested at 17%.
.
We can quickly check this. If $7,000 is invested at 20% then this produces $1400 of
interest (0.2*7000). Then if $14,000 is invested at 17%, this produces $2380 of interest (0.17*14000).
The total interest is then $1400 + $2380 = $3780 and this is the amount that the problem
said it should be. Therefore, our solution is good. The money invested at 20% is $7,000.
.
Hope this helps you to understand the problem.
(