Question
Duncan and his family are at the movies and wish to purchase some popcorn. A large popcorn costs $8 and a small popcorn costs $4. Duncan has offered to pay for the popcorn with the $22 in his wallet.
Select 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
Select 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 describe the situation with an inequality in standard form, we need to express the total cost of the popcorn in relation to the amount of money Duncan has.
Given:
- The cost of a large popcorn is $8. Hence, the total cost for \( x \) large popcorns is \( 8x \).
- The cost of a small popcorn is $4. Hence, the total cost for \( y \) small popcorns is \( 4y \).
- Duncan has $22 to spend.
We want to ensure that the total cost does not exceed the amount Duncan has:
\[
8x + 4y \leq 22
\]
This is the inequality in standard form, describing the limit on the total cost of the popcorn based on the quantities of large and small popcorns purchased.
Given:
- The cost of a large popcorn is $8. Hence, the total cost for \( x \) large popcorns is \( 8x \).
- The cost of a small popcorn is $4. Hence, the total cost for \( y \) small popcorns is \( 4y \).
- Duncan has $22 to spend.
We want to ensure that the total cost does not exceed the amount Duncan has:
\[
8x + 4y \leq 22
\]
This is the inequality in standard form, describing the limit on the total cost of the popcorn based on the quantities of large and small popcorns purchased.