Alicia runs a small business mowing yards in the summer. For every yard she mows, she earns $40. However, she spends part of this money on gasoline for her lawnmower. Each gallon of gasoline costs $3. Write an expression for the amount of money that Alicia earns in a day, where $y$ is the number of yards she mows and $g$ is the number of gallons of gasoline she buys.
A. $40y-$3g
B. $40y+$3g
C. $3g-$40y
D. $40g+$3y
Answer (1)
Alicia earns $40 for each yard she mows, so her earnings are 40 y .
She spends $3 for each gallon of gasoline, so her expenses are 3 g .
To find her net earnings, subtract the expenses from the earnings: 40 y − 3 g .
The expression for Alicia's earnings is $40 y − $3 g .
Explanation
Understanding the Problem Let's break down how to write an expression for Alicia's earnings. She makes money from mowing yards and spends money on gasoline. We need to represent both of these amounts and combine them to find her net earnings.
Calculating Earnings Alicia earns 40 f ore a c h y a r d s h e m o w s . I f s h e m o w s y$ yards, her total earnings from mowing are 40 \. y , which we can write as 40 y .
Calculating Expenses Alicia spends 3 f ore a c h g a ll o n o f g a so l in es h e b u ys . I f s h e b u ys g$ gallons of gasoline, her total cost for gasoline is 3 \. g , which we can write as 3 g .
Finding Net Earnings To find Alicia's net earnings, we subtract her expenses (the cost of gasoline) from her earnings (the money from mowing yards). So, her net earnings are 40 y − 3 g . This means the correct expression is $40 y − $3 g .
Examples
Imagine Alicia is saving up to buy a new lawnmower that costs $500. She mows 15 yards a day and uses 2 gallons of gasoline. Using the expression 40 y − 3 g , we can calculate her daily earnings: $40(15) - 3(2) = 600 - 6 = $594. We can then determine how many days she needs to work to save enough money for the new lawnmower. This kind of calculation is useful for budgeting and planning in many small businesses.
