Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Sadie, a caterer, is investing some money in equipment and employees to help grow her business. Recently she spent $51 on equipment and hired a server who makes $14 per hour. Sadie is hoping to make up these expense at the next job that is scheduled, which pays a base of $48 in addition to $15 per hour that the server works. In theory, this event could pay enough to cancel out Sadie's expenditures. How much would the job pay? How long would the job have to be? The expenditures and pay would both be $_____ if the job lasted for _____ hours.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Sadie, a caterer, is investing some money in equipment and employees to help grow her business. Recently she spent $51 on equipment and hired a server who makes $14 per hour. Sadie is hoping to make up these expense at the next job that is scheduled, which pays a base of $48 in addition to $15 per hour that the server works. In theory, this event could pay enough to cancel out Sadie's expenditures. How much would the job pay? How long would the job have to be?   The expenditures and pay would both be $_____ if the job lasted for _____ hours.

Bytelearn · Accepted Answer

Define variables: Define the variables. Let's define the number of hours the server works as 'h'. Sadie's expenditures for equipment and the server's hourly wage are given as $51 and $14 per hour, respectively. Sadie's pay for the job is a base of $48 plus $15 per hour worked by the server.Write expenditure equation: Write the equation for Sadie's expenditures. Sadie's total expenditures (E) can be calculated by adding the cost of equipment to the server's wage multiplied by the number of hours worked. E = $51 + $14hWrite pay equation: Write the equation for Sadie's pay for the job. Sadie's total pay (P) from the job is the base pay plus the hourly rate multiplied by the number of hours the server works. P = $48 + $15hSet up cancellation equation: Set up the equation to find when Sadie's expenditures and pay cancel out. To find when Sadie's expenditures and pay cancel out, we set the expenditure equation equal to the pay equation. $51 + $14h = $48 + $15hSolve for 'h': Solve the equation for 'h'. Now we will solve for 'h' to find out how many hours the job would need to last for the expenditures and pay to be equal. $51 + $14h = $48 + $15h Subtract $14h from both sides: $51 = $48 + $15h - $14h $51 = $48 + $1h Subtract $48 from both sides: $51 - $48 = $1h $3 = $1h Divide both sides by $1: h = 3Calculate total pay: Calculate the total pay for the job. Now that we know the job lasts for 3 hours, we can calculate the total pay. P = $48 + $15h P = $48 + $15(3) P = $48 + $45 P = $93

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