system of linear equation

Question

Juan invests a total of $27,000 in two accounts. The first account earned a rate of return of 9% (after a year). However, the second account suffered a 2% loss in the same time period. At the end of one year, the total amount of money gained was $1,055.00. How much was invested into each account?

Answer 1

1. x ... let this be the amount put into the first account
2. y ... let this be the amount put int the second account
3. x + y = 27000 ... this is the first linear equation
4. x(0.09) ... this is the amount gained by the first account
5. -y(0.02) ... this is the amount lost by the second account
6. x(0.09) -y(0.02) = 1055 ... this is the second linear equation
7. equations 3 and 6 are your system of equations (two equations and two unknowns)
8. x = 27000 - y ... solving eq. 3 for x
9. (27000 - y)(0.09) - y(0.02) = 1055 ... subbing eq. 8 in to eq. 6
10. y = 12500 ... solving eq. 9 for y (a few simple steps left out here,of course)
11. x = 27000 - 12500 ... subbing eq. 10 into eq. 8
12. x = 14500 ... solving for x.
13. So there was $14,500 and $12,500 originally invested into the first and second accounts, respectively
14. This can be verified by adding the 9% gain by the first account ((0.09)(14500)) to the 2% loss by the second account (-(0.02)(12500)) to get (0.09)(14500) + (- (0.02)(12500) = 1055.

Answer 2

0.09x - 0.02(27000 - x) = 1055

Can you solve for x and answer?