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In Mathematics / College | 2025-07-04

Select the correct answer.
A ski rental store rents a pair of skis for $44 a day and a snowboard for $58 a day. Yesterday, the store made $2,232 on ski and snowboard rentals. They rented 9 more pairs of skis than snowboards. Write a system of equations that could be used to represent this situation and to find the number of ski rentals and snowboard rentals.

A. [tex]$\begin{array}{l}44 x+58 y=2,232 \\ y=x+9\end{array}$[/tex]
B. [tex]$\begin{array}{l}44 x+58 y=2,232 \\ x+y=9\end{array}$[/tex]
C. [tex]$44 x+58 y=2,232 \\ y=x-9$[/tex]
D. [tex]$\begin{array}{l}44 x+58 y=2,232 \\ x=y-9\end{array}$[/tex]

Asked by fatimitapau2008

Answer (2)

The correct system of equations representing the ski rental situation is: 44x + 58y = 2232 and x = y + 9. Therefore, the correct answer is option A. This reflects the total revenue and the relationship of the rentals.
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Answered by Anonymous | 2025-07-04

Define x as the number of ski rentals and y as the number of snowboard rentals.
Write the equation for the total revenue: 44 x + 58 y = 2232 .
Express the relationship between ski and snowboard rentals: x = y + 9 .
The correct system of equations is: 44 x + 58 y = 2232 and x = y + 9 .

Explanation

Define variables and write the revenue equation Let x be the number of ski rentals and y be the number of snowboard rentals. The total revenue from ski rentals is 44 x and from snowboard rentals is 58 y . The total revenue yesterday was $2232 , so we have the equation

Revenue equation 44 x + 58 y = 2232

Write the relationship between ski and snowboard rentals We are also given that they rented 9 more pairs of skis than snowboards. This means that the number of ski rentals is 9 more than the number of snowboard rentals. So, we can write this as

Relationship equation x = y + 9

System of equations Now we have a system of two equations with two variables:


Examples
Understanding systems of equations is crucial in many real-world scenarios. For instance, imagine you're planning a balanced diet. You need to meet certain nutritional requirements (like calories and protein) by combining different foods. Each food contributes differently to these requirements, and you can set up a system of equations to find the right amounts of each food to eat. Similarly, in business, you might use systems of equations to optimize production costs or manage inventory levels, ensuring you meet demand while minimizing expenses. These mathematical tools help in making informed decisions and achieving desired outcomes in various aspects of life.

Answered by GinnyAnswer | 2025-07-04

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