Question

Complete the equation or inequality you would use to find how many hours each brother works in a month given the information that Roger earns $3,240 per month working x hours and his brother works 20 hours more than Roger and earns $5,400 per month.

Answer 1

To solve for the number of hours Roger and his brother work, we establish two equations based on their salaries and set them equal since they earn the same hourly wage. Solving these will give the hours Roger works as 'x' and his brother as 'x + 20'.

Step-by-step explanation:

To find out how many hours each brother works in a month, we will use the equations based on their monthly earnings and the number of hours they work. Since we have Roger earning $3,240 per month working x hours, we can establish his hourly wage as $3,240/x. His brother works 20 hours more than Roger, which would be x + 20 hours, and earns $5,400 per month. The equation for Roger's salary then becomes $3,240/x = hourly wage, and for his brother, it would be $5,400/(x + 20) = hourly wage.

Assuming they are paid the same hourly rate, we set the equations equal to each other:

$3,240/x = $5,400/(x + 20).

From this, we can solve for x, which will give us the number of hours Roger works, and adding 20 to this will give us the number of hours his brother works.