### Building A House  I was organising the construction of my house and I received the following bill:

\$1,100 for the painter and decorator

\$1,100 for the electrician and the plumber

\$1,700 for the painter and the plumber

\$3,200 for the painter and the bricklayer

\$3,300 for the carpenter and the electrician

\$5,300 for the carpenter and the bricklayer

What did each person charge for their services?

Scroll down for a clue and further down for the answer.

*

*

*

*

*

*

*

Clue:

We can turn each bill into an equation:

PA + D = 1100

E + PL = 1100

PA + PL = 1700

PA + B = 3200

C + E = 3300

C + B = 5300

*

*

*

*

*

*

*

Decorator = \$200

Electrician = \$300

Plumber = \$800

Painter = \$900

Bricklayer = \$2,300

Carpenter = \$3,000

We can turn each bill into an equation:

PA + D = 1100

E + PL = 1100

PA + PL = 1700

PA + B = 3200

C + E = 3300

C + B = 5300

We can now join some equations together to solve them:

From C + E = 3300 and C + B = 5300

B – E = 2000

From E + PL = 1100 and PA + B = 3200

E + PL + PA + B = 4300

From E + PL = 1100 and PA + B = 3200 and PA + PL = 1700

B + E = 2600

Adding the results of the 1st and 3rd equation we have derived gives us:

2B = 4600

This means B = 2300.

By substituting this value into the other equations, we determine the other values.