They system of equations

Question

n = 35 + p
2.5n + 3.5p = 825.5

can be used to determine the number of $2.50 pizza slices n and $3.50 pizza pockets p sold in the cafeteria in a single day. Use the graph of the system below to estimate the number of pizza pockets sold.

Question 8 options:

Approximately 125 pizza pockets were sold.

Approximately 155 pizza pockets were sold.

Approximately 235 pizza pockets were sold.

Approximately 300 pizza pockets were sold.

Answer 1

To solve the system of equations provided and estimate the number of pizza pockets sold, we can first express both equations and solve for \( n \) and \( p \).

1. The equations from the problem are:

   \[ n = 35 + p \]

   \[ 2.5n + 3.5p = 825.5 \]

2. Substitute the first equation into the second equation:

   \[ 2.5(35 + p) + 3.5p = 825.5 \]

   This expands to:

   \[ 87.5 + 2.5p + 3.5p = 825.5 \]

   Combine like terms:

   \[ 87.5 + 6p = 825.5 \]

   Subtract 87.5 from both sides:

   \[ 6p = 738 \]

   Now, divide by 6:

   \[ p = 123 \]

So, the estimated number of pizza pockets sold is approximately 125 pizza pockets. Thus, the answer is:

Approximately 125 pizza pockets were sold.