Name___________________
DSPM 0800 HOMEWORK (ASSIGNMENT 9, SECTION 10-4)
Solve the following problems using systems of equations:
1. Emily Harrington made two 1-year investments totaling $7,000 at interest rates of 4%
and 7%. If she received $415 in return, how much money was invested at each rate?
Let x = the amount invested at 4%.
y = the amount invested at 7%.
Since the two investments totaled $7,000,
x + y = 7,000
Since the total interest is $415,
0.04 0.07 415 (Note that we change percents to decimals)x y
Since it is easy to express one variable in terms of the other, we can solve by the
substitution method. (You can still use the addition method for this system.)
Let y = 7,000 – x. (If you choose to let x = 7,000 – y, the calculations will be
similar.) Then
0.04 0.07(7, 000 ) 415
0.04 490 0.07 415
0.03 490 415
0.03 490 490 415 490
0.03 75
2,500
x x
x x
x
x
x
x
If you cleared decimals, the computation would look like this:
0.04 0.07(7, 000 ) 415
4 7(7, 000 ) 41,500
4 49, 000 7 41,500
3 49,000 41,500
3 49, 000 49,000 41,500 49,000
3 7,500
2,500
x x
x x
x x
x
x
x
x
Therefore, y = 7,000 – 2,500 = 4,500.
