Applications of linear equations

Question

Jim builds benches in his spare time. Good quality plywood costs $4.50 per square foot. There is approximately a 10% waste of material due to cutting and fitting. He also figures $275 per month for finishing material,glue,tools,etc. If he charges $10.10 per square foot of finished product, how many square feet of plywood did he buy originally if his profit is $110.56 in one month?

Answer 1

Hi Haven,

I got 74.87 square feet. We know $10.10 is how much Jim charges as revenue for each square foot of fencing. $4.50/ square foot is what it costs Jim, along with a 10% increase in the $4.50 due to waste. It also costs Jim $275 that goes towards buying additional supplies for building the fence that month. The profit for that month is $110.56. Therefore, this is my equation:

f is the square feet of fencing

10.10f-(275+(1+0.1)*4.5f) = 110.56 => 5.15f-275 = 110.56 => 74.87

Answer 2

Profit = Income - Expenses

x = Total square feet of plywood purchased

Expenses = ($4.50)x + $275

10% of the plywood is wasted so only 90% is used.

Income = ($10.10)(.90)x

Income = ($9.09)x

Profit = Income - Expenses

Profit = ($9.09)x - [ ($4.50)x + $275 ]

Profit = ($9.09)x - ($4.50)x - $275

Profit = $4.59x - $275

Find x if profit = $110.56

110.56 = 4.59x - 275

385.56 = 4.59x

x = (385.56) / (4.59)

x = 84

He originally purchased 84 square feet of plywood.