Question

Luke's Bakery recently spent a total of $69 on new equipment, and their average hourly operating costs are $15. Their average hourly receipts are $39. The bakery will soon make back the amount it invested in equipment. How many hours will that take? What would the total expenses and receipts both equal?

Answer 1

Answer:

It will take the bakery 2.875 hours to make back the amount invested.

The total expenses and receipts, both will = $112.125

Step-by-step explanation:

Given:

Cost of equipment = $69

Operation cost per hour = $15

Average hourly receipts = $39

To find how many hours will it take for the Bakery to make back the amount invested and what would the total expenses and receipts both equal

Solution:

Let the bakery take $t$ hours to make back the amount invested.

Operation cost for $t$ hours in dollars will be = $15t$

Equipment cost = $69

Total expenses in dollars can be given as = $15t+69$

Receipts for $t$ hours in dollars will be = $39t$

Since the bakery makes up the amount invested in $t$ hours, so the amount in expenses must be equal to the total receipts for $t$ hours.

Thus, we have:

$39t=15t+69$

Subtracting both sides by $15t$

$39t-15t=15t-15t+69$

$24t=69$

Dividing both sides by 24.

$\frac{24t}{24}=\frac{69}{24}$

∴ $t=2.875$

So, in 2.875 hours the bakery will be able to make back all the investment.

Total expenses in 2.875 hours will be = $15(2.875)+69=43.125+69=\ 112.125$

Total receipts will be the same and can be given as = $39\times 2.875 = \ 112.125$