Question

Pete's Plumbing charges 25x + 50 dollars for x hours of work. Plugged Pipes charges 50x + 75

dollars for the same number of hours.

a. Write an expression in simplest form to represent how much more Plugged Pipes costs
than Pete's Plumbing for x hours of work.

b. If they each work for 2 hours, how much more expensive is Plugged Pipes?

Answer 1

a. To find out how much more expensive Plugged Pipes is than Pete's Plumbing, we need to subtract Pete's Plumbing's cost from Plugged Pipes' cost. The expression for the difference in cost is:

(50x + 75) - (25x + 50) = 25x + 25

This is the simplified form of the expression that represents the difference in cost.

b. If they each work for 2 hours, we can substitute x = 2 into the expressions for their costs and compare the results:

Plugged Pipes: 50(2) + 75 = 125 dollars

Pete's Plumbing: 25(2) + 50 = 100 dollars

So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.

Explanation:

Sure, here is a step-by-step explanation of how to find the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work:

1. Start with the expression for the cost of Plugged Pipes: 50x + 75
2. Subtract the expression for the cost of Pete's Plumbing: 25x + 50
3. To do this, we need to distribute the subtraction (-) sign to the x and the constant terms: (50x + 75) - (25x + 50)
4. Next, we'll combine like terms: 50x - 25x + 75 - 50 = 25x + 25
5. The final expression, 25x + 25, represents the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work.

To find out how much more expensive Plugged Pipes is for 2 hours of work we can substitute x = 2 into the expression for their costs and compare the results:

Plugged Pipes: 50(2) + 75 = 125 dollars

Pete's Plumbing: 25(2) + 50 = 100 dollars

So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.