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

This equation represents the data:
\[2.5(12.75x + 24.50) = 188.75\]

Big Time Movers worked $[/tex]\square$ hours on New Year's Day.



Answer :

GinnyAnswer
Let's solve the problem step-by-step.

Given:
- The initial fee for Big Time Movers is [tex]\( \$24.50 \)[/tex].
- The hourly rate for their moving services is [tex]\( \$12.75 \)[/tex].
- On holidays, the charge is 2.5 times the regular total amount.
- They earned [tex]\( \$188.75 \)[/tex] on New Year's Day.

We need to find the number of hours they worked, denoted as [tex]\( x \)[/tex].

We start with the equation:
[tex]\[ 2.5 \times (12.75x + 24.50) = 188.75 \][/tex]

First, we'll isolate the expression inside the parentheses by dividing both sides by 2.5:
[tex]\[ 12.75x + 24.50 = \frac{188.75}{2.5} \][/tex]

Calculate the division on the right-hand side:
[tex]\[ 12.75x + 24.50 = 75.50 \][/tex]

Next, isolate the term with [tex]\( x \)[/tex] by subtracting [tex]\( 24.50 \)[/tex] from both sides:
[tex]\[ 12.75x = 75.50 - 24.50 \][/tex]

Perform the subtraction:
[tex]\[ 12.75x = 51.00 \][/tex]

Now, solve for [tex]\( x \)[/tex] by dividing both sides by the hourly rate [tex]\( 12.75 \)[/tex]:
[tex]\[ x = \frac{51.00}{12.75} \][/tex]

Finally, calculate the division to find [tex]\( x \)[/tex]:
[tex]\[ x = 4.0 \][/tex]

Therefore, Big Time Movers worked [tex]\(\boxed{4.0}\)[/tex] hours on New Year's Day.

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