A principal has given a class $75 to help pay for the field trip to a zoo. The students in class are selling pies for $5 each to earn the rest of the money they need. The field trip will cost a total of $386. Which inequality can be used to find p, the number of pies the class needs to sell in order to earn enough money to pay for the field trip?

Question

A. 5px + 75 ≤ 386
B. 5p + 75 ≥ 386
C. 75p + 5 ≥ 386
D. 75p + 5 ≤ 386
Show your work

Answer 1

To find the correct inequality representing the situation, we start by identifying the components involved:

1. The total cost of the field trip is $386.
2. The principal has provided the class with $75.
3. The class sells pies at a price of $5 each, and we let \( p \) represent the number of pies sold.

To determine how much more money the class needs to raise to cover the total cost of the trip, we first subtract the funds provided by the principal from the total cost:

\[ \text{Required additional funds} = 386 - 75 \]

Now, calculating that gives us:

\[ \text{Required additional funds} = 311 \]

This means that the class needs to raise at least $311 from selling pies. Since each pie sells for $5, if we let \( p \) represent the number of pies sold, the money earned from selling \( p \) pies is:

\[ \text{Money from pies} = 5p \]

To ensure they raise enough money, the money from selling pies must be at least the additional funds required. Thus, we can set up the inequality:

\[ 5p \geq 311 \]

However, we need to make sure that the total funds (from both the pies and the principal) meet or exceed the total trip cost ($386). This leads us to formulate the total funds as follows:

\[ 75 + 5p \geq 386 \]

Now, if we rearrange this inequality, we can write it in terms of \( p \):

\[ 5p + 75 \geq 386 \]

This matches the format of option B provided in your choices. Therefore, the correct inequality to find \( p \), the number of pies the class needs to sell, is:

\[ \text{B. } 5p + 75 \geq 386 \]