Question

Which system of equations represents the following situation?

Mrs. Stevens bought 3 containers of yogurt and 5 oranges for $2.79. The next week she bought 4 containers of yogurt and 7 oranges for $3.81, paying the same price each week.

A)
5x + 3y = 2.79
4x + 7y = 3.81

B)
x + y = 2.79
x + y = 3.81

C)
3x + 5y = 2.79
4x + 7y = 3.81

D)
x + y = 8
3x + 5y = 2.79

Answer 1

The correct system of equations is option C: 3x + 5y = 2.79 and 4x + 7y = 3.81, representing the price of yogurt (x) and oranges (y).

Step-by-step explanation:

The system of equations that represents the situation where Mrs. Stevens bought 3 containers of yogurt and 5 oranges for $2.79, and the next week bought 4 containers of yogurt and 7 oranges for $3.81, is given by option C, which is:

3x + 5y = 2.79
4x + 7y = 3.81

In these equations, x represents the price of one container of yogurt and y represents the price of one orange. Since the price of yogurt and oranges remained the same across the two weeks, we model each week's total cost as a linear combination of the number of each item purchased. The coefficients in front of x and y correspond to the number of yogurt containers and the number of oranges purchased each week, respectively.