Maria and Liam work in a banquet hall. Maria earns a 20% commission on her food sales. Liam earns a weekly salary of $625 plus a 10% commission on his food sales. What amount of fo... Maria and Liam work in a banquet hall. Maria earns a 20% commission on her food sales. Liam earns a weekly salary of $625 plus a 10% commission on his food sales. What amount of food sales will result in Maria and Liam earning the same amount for the week?
Understand the Problem
The question is asking us to find a specific amount of food sales that will make the earnings of Maria and Liam equal for the week. We will need to set up equations based on their earning structures and solve for the food sales amount.
Answer
The amount of food sales is $6250.
Answer for screen readers
The amount of food sales that will result in Maria and Liam earning the same amount for the week is $6250.
Steps to Solve
- Define Variables for Food Sales
Let ( x ) represent the total food sales amount for both Maria and Liam.
- Set Up Maria's Earnings Equation
Maria earns 20% commission on her food sales. Therefore, her earnings can be represented as: $$ \text{Maria's Earnings} = 0.20x $$
- Set Up Liam's Earnings Equation
Liam has a fixed salary of $625 plus a 10% commission on his food sales. His earnings can be expressed as: $$ \text{Liam's Earnings} = 625 + 0.10x $$
- Set the Equations Equal
To find the amount of food sales that makes their earnings equal, set Maria's earnings equal to Liam's: $$ 0.20x = 625 + 0.10x $$
- Isolate ( x )
Subtract ( 0.10x ) from both sides of the equation: $$ 0.20x - 0.10x = 625 $$
This simplifies to: $$ 0.10x = 625 $$
- Solve for ( x )
Divide both sides by ( 0.10 ): $$ x = \frac{625}{0.10} $$
This results in: $$ x = 6250 $$
The amount of food sales that will result in Maria and Liam earning the same amount for the week is $6250.
More Information
Maria and Liam's earning structures illustrate a common scenario in commission-based jobs, highlighting how combinations of salary and commission can affect overall earnings. This problem also demonstrates the use of algebra to solve for an unknown.
Tips
- Forgetting to convert the percentages into decimals when calculating commissions.
- Not isolating the variable correctly when setting up the equation.
- Misapplying arithmetic operations when manipulating the equation.
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