Answer:
We have a total investment of $20,000 in two different amounts A and B.
Then:
A + B = $20,000.
And we know that the interest of the amount A is 7%, and the interest of the amount B is 10%. (i will assume that both interests are yearly interest)
And after one year, Hank earns $1,640 thanks to those interests, then we have that:
(7%/100%)*A + (10%/100%)*B = $1,640
And we can write this as:
0.07*A + 0.1*B = $1,640
Then we have a system of equations:
A + B = $20,000
0.07*A + 0.1*B = $1,640
To solve this, the first step is isolating one of the variables in one of the equations.
Let's isolate A in the first equation:
A + B = $20,000
A = $20,000 - B.
Now we can replace this in the other equation:
0.07*A + 0.1*B = $1,640
0.07*($20,000 - B) + 0.1*B = $1,640
$1,400 - 0.07*B + 0.1*B = $1,640
0.03*B = $1,640 - $1,400 = $240
B = $240/0.03 = $12,000
Then we have:
A = $20,000 - $12,000 = $8,000
Hank invests $12,000 in the 10% account and $8,000 in the 7% one.
