Denise bought 116 ounces of beans for a bean dip. She bought both 15-ounce cans and 28-ounce cans, and the total number of cans she bought was 6. Which of these systems of equations can be used to determine the number of 15-ounce cans and the number of 28-ounce cans that she bought? Assume x represents the number of 15-ounce cans and y represents the number of 28-ounce cans.

Question

x + y = 6. 15 x + 28 y = 116.
x + y = 6. 28 x + 15 y = 116.
x + y = 116. 15 x + 28 y = 6.
x + y = 116. 28 x + 15 y = 6.

Answer 1

To solve for the number of 15-ounce and 28-ounce cans that Denise bought using a system of equations, we define:

• \( x \) as the number of 15-ounce cans
• \( y \) as the number of 28-ounce cans

We are given two pieces of information:

1. The total number of cans (15-ounce and 28-ounce) is 6.
2. The total weight of the beans is 116 ounces.

Based on this information, we can set up the following equations:

1. The equation that represents the total number of cans is: \[ x + y = 6 \]

2. The equation that represents the total weight of the beans is: \[ 15x + 28y = 116 \]

Therefore, the correct system of equations that can be used to determine the number of 15-ounce cans and the number of 28-ounce cans Denise bought is:

\[ \begin{align*} x + y &= 6 \ 15x + 28y &= 116 \end{align*} \]

Thus, the first option is the correct one: x + y = 6. 15x + 28y = 116.