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. [tex]$40 g+$[/tex][tex]$3 y$[/tex]
B. [tex]$3 g-$[/tex][tex]$40 y$[/tex]
C. [tex]$40 y+$[/tex][tex]$3 g$[/tex]
D. [tex]$40 y-$[/tex][tex]$3 g$[/tex]
Answer (2)
Alicia's earnings from mowing y yards are calculated as 40 y .
Her expenses on g gallons of gasoline are 3 g .
Her net earnings are found by subtracting the expenses from the earnings: 40 y − 3 g .
The expression representing Alicia's net earnings is $40 y − $3 g .
Explanation
Problem Analysis Let's analyze the problem. Alicia earns money for each yard she mows and spends money on gasoline. We need to find an expression that represents her net earnings, which is the money she earns minus the money she spends.
Calculating Earnings Alicia earns 40 f ore a c h y a r d s h e m o w s . I f s h e m o w s y$ yards, her total earnings are 40 × y , which can be written 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 spending is 3 × g , which can be written as 3 g .
Finding Net Earnings To find Alicia's net earnings, we subtract her expenses (gasoline cost) from her earnings (mowing yards). So, the expression for her net earnings is 40 y − 3 g .
Final Answer Therefore, the amount of money that Alicia earns in a day is given by the expression $40 y − $3 g .
Examples
Imagine Alicia is not just mowing yards but also selling lemonade. If each yard mowed brings in $40 and each lemonade sold costs $3 to make (ingredients, cup), the expression 40 y − 3 g helps Alicia calculate her daily profit, where 'y' is the number of yards mowed and 'g' is the number of lemonades sold. This kind of calculation is crucial for any small business to understand their profitability and manage their expenses effectively.
Alicia's earnings in a day can be expressed as the total money she makes from mowing yards minus her gasoline expenses. The formula for her net earnings is given by $40y - $3g, where $40y represents her earnings from mowing y yards, and $3g represents her expenses for g gallons of gasoline. Thus, the correct choice is option D.
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