Avery and her family are at the movies and wish to purchase some popcorn. A large popcorn costs $6 and a small popcorn costs $3. Avery has offered to pay for the popcorn with the $26 in her wallet.

Question

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

Answer 1

To describe the situation involving the purchase of popcorn in terms of an inequality, we can express the total cost of the popcorns in relation to the amount of money Avery has.

Given:

• A large popcorn costs $6, so the cost for \( x \) large popcorns is \( 6x \).
• A small popcorn costs $3, so the cost for \( y \) small popcorns is \( 3y \).
• Avery has $26 to spend.

The total cost of the popcorn must be less than or equal to the amount Avery has. This can be expressed with the following inequality:

\[ 6x + 3y \leq 26 \]

This inequality represents the situation where \( x \) is the number of large popcorns and \( y \) is the number of small popcorns, while ensuring that the total cost does not exceed $26.

To convert it into standard form, we can rearrange it as:

\[ 6x + 3y - 26 \leq 0 \]

This can also be expressed as:

\[ 6x + 3y \leq 26 \] (which is already in a commonly used format).

Thus, the final inequality in standard form is:

\[ 6x + 3y \leq 26 \]