Question

A roofing contractor buys 30 bundles of shingles and 4

rolls of roofing paper for $1040.

In a second purchase (at the same prices), the

contractor buys 12 bundles of shingles and 16 rolls of

roofing paper for $2000.

Create and solve a system of equations in order to

determine how much each bundle of shingles (x) and

roll of roofing paper (y) would cost

Answer 1

Answer:

Cost of one bundle of shingles is $20 and cost of one roll of roofing paper is $110.

Step-by-step explanation:

Let the cost of each bundle of shingles = x

And cost of the roofing paper = y

Contractor buys 30 bundles of shingles and 4 rolls of roofing paper for $1040.

30x + 4y = 1040

15x + 2y = 520 -----(1)

In a second purchase contractor buys 12 bundles of shingles and 16 rolls of roofing paper for $2000

12x + 16y = 2000

3x + 4y = 500 --- (2)

Equation (1) multiplied by 2 then subtracted from equation (2)

(3x + 4y) - 2(15x + 2y) = 500 - 1040

(3x - 30x) + (4y - 4y) = -540

-27x = -540

x = 20

From equation (1)

15(20) + 2y = 520

300 + 2y = 520

2y = 220

y = 110

Therefore, cost of one bundle of shingles is $20 and cost of one roll of roofing paper is $110.