Big Time Movers charges an initial fee of $24.50, plus $12.75 an hour for their moving services. On holidays, they charge 2.5 times their regular total amount. If they made $188.75 on a job on New Year’s Day, how many hours did they work?

Question

This equation represents the data:

2.5(12.75x + 24.50) = 188.75

Big Time Movers worked
hours on New Year’s Day.

Answer 1

To find out how many hours Big Time Movers worked on New Year's Day, we can solve the equation you provided:

\[ 2.5(12.75x + 24.50) = 188.75 \]

First, we will divide both sides of the equation by 2.5:

\[ 12.75x + 24.50 = \frac{188.75}{2.5} \]

Now, calculate \( \frac{188.75}{2.5} \):

\[ 188.75 \div 2.5 = 75.5 \]

So we have:

\[ 12.75x + 24.50 = 75.5 \]

Next, we will subtract 24.50 from both sides:

\[ 12.75x = 75.5 - 24.50 \]

Calculating \( 75.5 - 24.50 \):

\[ 75.5 - 24.50 = 51 \]

Now we have:

\[ 12.75x = 51 \]

Next, we will divide both sides by 12.75:

\[ x = \frac{51}{12.75} \]

Calculating \( \frac{51}{12.75} \):

\[ x = 4 \]

Thus, Big Time Movers worked 4 hours on New Year’s Day.