A contractor planning the construction of a house found that he would have to pay:
$1,100 to the Paper Hanger and the Painter,
$1,700 to the Plumber and the Painter,
$1,100 to the Plumber and the Electrician,
$3,300 to the Electrician and the Carpenter,
$5,300 to the Carpenter and the Mason,
$3,200 to the Mason and the Painter.
What does each man charge for his services?
Solution to the Problem:
The answer is:$900 to the Painter,
$200 to the Paper Hanger,
$800 to the Plumber,
$300 to the Electrician,
$3,000 to the Carpenter,
$2,300 to the Mason.
Let PH = amount charged by the Paper Hanger
Let PA = amount charged by the Painter
Let PL = amount charged by the Plumber
Let C = amount charged by the Carpenter
Let E = amount charged by the Electrician
Let M = amount charged by the Mason
Then we can set up the following six equations with 6 unknowns:
1) PH + PA = 1100
2) PL + PA = 1700
3) PL + E = 1100
4) E + C = 3300
5) C + M = 5300
6) M + PA = 3200
Now, solve these six equations (the numbers of the equations which are added or subtracted are in parentheses).
M - E = 2000 (5 - 4)
M + PA + PL + E = 4300 (3 + 6)
M + E = 2600 (3 + 6 - 2)
2M = 2600 (adding the results of 5 - 4 and 3 + 6 - 2)
So, M = 2300.
Now, substitute back to get the other five values.
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Shaylynn Martin |
Mountain View High School, Mountain View, Wyoming |