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In Mathematics / College | 2025-07-05

A coffee shop sells regular and large coffees. A regular coffee costs $3, and a large coffee costs $5. If the shop sells 50 coffees and collects $180, what system of equations represents the situation?
a. $5x+3y=50, x+y=180$
b. $3x+5y=180, x+y=50$
c. $3x+5y=50, x+y=180$
d. $5x+3y=180, x+y=50

Asked by linagalaz5

Answer (2)

Define x as the number of regular coffees and y as the number of large coffees.
Write the equation for the total number of coffees sold: x + y = 50 .
Write the equation for the total amount collected: 3 x + 5 y = 180 .
The system of equations that represents the situation is: 3 x + 5 y = 180 , x + y = 50 ​ .

Explanation

Problem Analysis Let's analyze the problem. We are given the prices of two types of coffees, the total number of coffees sold, and the total amount of money collected. We need to find the system of equations that represents this situation.

Setting up the Equations Let x be the number of regular coffees sold and y be the number of large coffees sold. The total number of coffees sold is 50, so we have the equation x + y = 50 The total amount collected is $180 . The amount collected from regular coffees is $3 x , and the amount collected from large coffees is $5 y . So we have the equation 3 x + 5 y = 180 Therefore, the system of equations is x + y = 50 3 x + 5 y = 180

Finding the Correct Option Comparing this system of equations with the given options, we see that option b matches our system of equations.

Final Answer Therefore, the correct answer is b. 3 x + 5 y = 180 , x + y = 50 .


Examples
This type of problem is useful in business when you want to determine the number of items sold given the total revenue and the prices of the items. For example, a bakery sells cakes for $20 and pies for $15 . If they sold a total of 80 items and collected $1350 , you can set up a system of equations to find out how many cakes and pies they sold. Let c be the number of cakes and p be the number of pies. Then c + p = 80 and 20 c + 15 p = 1350 . Solving this system will give you the number of cakes and pies sold.

Answered by GinnyAnswer | 2025-07-05

To represent the coffee shop's sales with a system of equations, we define x as the number of regular coffees and y as the number of large coffees. The system of equations is x + y = 50 and 3 x + 5 y = 180 , making option b the correct choice. Therefore, the answer is option b: 3 x + 5 y = 180 , x + y = 50 .
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Answered by Anonymous | 2025-07-09

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