Question
Devin and his family are at the movies and wish to purchase some popcorn. A large popcorn costs $6 and a small popcorn costs $2. Devin has offered to pay for the popcorn with the $19 in his wallet.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of large popcorns
y = the number of small popcorns
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of large popcorns
y = the number of small popcorns
Answers
GPT-4o mini
To create an inequality in standard form that represents the situation, we can start by using the costs of the large and small popcorn.
- A large popcorn costs $6, so the total cost for \( x \) large popcorns would be \( 6x \).
- A small popcorn costs $2, so the total cost for \( y \) small popcorns would be \( 2y \).
Devin has $19 to spend, so the total cost of the popcorn must not exceed this amount. Therefore, we can set up the inequality:
\[
6x + 2y \leq 19
\]
To write this inequality in standard form \( Ax + By \leq C \), we can rearrange it as follows:
\[
6x + 2y - 19 \leq 0
\]
Thus, the standard form of the inequality is:
\[
6x + 2y \leq 19
\]
This describes all combinations of large and small popcorns that Devin can buy without exceeding his budget of $19.
- A large popcorn costs $6, so the total cost for \( x \) large popcorns would be \( 6x \).
- A small popcorn costs $2, so the total cost for \( y \) small popcorns would be \( 2y \).
Devin has $19 to spend, so the total cost of the popcorn must not exceed this amount. Therefore, we can set up the inequality:
\[
6x + 2y \leq 19
\]
To write this inequality in standard form \( Ax + By \leq C \), we can rearrange it as follows:
\[
6x + 2y - 19 \leq 0
\]
Thus, the standard form of the inequality is:
\[
6x + 2y \leq 19
\]
This describes all combinations of large and small popcorns that Devin can buy without exceeding his budget of $19.