Question

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.
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 determine the number of 15-ounce cans (x) and 28-ounce cans (y) that Denise bought, we can set up the equations based on the information provided.

1. The total number of cans she bought is 6, which gives us the first equation:
\[
x + y = 6.
\]

2. The total weight of the beans is 116 ounces, which gives us the second equation. Each 15-ounce can contributes \(15x\) ounces, and each 28-ounce can contributes \(28y\) ounces, leading to:
\[
15x + 28y = 116.
\]

Putting these two equations together gives us the following system of equations:
\[
\begin{align*}
x + y & = 6, \\
15x + 28y & = 116.
\end{align*}
\]

Thus, the correct system of equations is:
\[
x + y = 6 \quad \text{and} \quad 15x + 28y = 116.
\]

So the first option is the correct choice:
**x + y = 6, 15x + 28y = 116.**