Questions: Luke works at a store and earns a fixed amount of 126 plus 56.39 per sale. Noah works at a different store and earns a fixed amount of 333 plus 28.24 per sale. They both made the same number of sales, but Luke earned 5/3 as much money as Noah this week. Write the equation that can be used to find the number of sales Luke made this week. Represent the number of sales as x and don't use any symbols.

Solution Steps

To find the number of sales \( x \) that Luke made, we need to set up an equation based on the given information. Luke's total earnings can be expressed as \( 126 + 56.39x \), and Noah's total earnings as \( 333 + 28.24x \). According to the problem, Luke's earnings are \(\frac{5}{3}\) times Noah's earnings. Therefore, we can set up the equation:

\[ 126 + 56.39x = \frac{5}{3} \times (333 + 28.24x) \]

To find the number of sales \( x \) that Luke made, we start by setting up the equation based on the given information. Luke's earnings are given by:

\[ 126 + 56.39x \]

Noah's earnings are given by:

\[ 333 + 28.24x \]

According to the problem, Luke's earnings are \(\frac{5}{3}\) times Noah's earnings. Therefore, the equation is:

\[ 126 + 56.39x = \frac{5}{3} \times (333 + 28.24x) \]

Simplify the right side of the equation:

\[ \frac{5}{3} \times (333 + 28.24x) = 555 + 47.0667x \]

Now, the equation becomes:

\[ 126 + 56.39x = 555 + 47.0667x \]

Rearrange the equation to solve for \( x \):

\[ 56.39x - 47.0667x = 555 - 126 \]

\[ 9.3233x = 429 \]

Divide both sides by 9.3233 to find \( x \):

\[ x = \frac{429}{9.3233} \approx 46.01 \]

Final Answer