Makenzie got a $30 gift certificate to the local theater for her birthday. Adult tickets (x) cost $8.00 and tickets for children (y) cost $4.50.

Question

Which inequality represents the number of adults and children who can go to a show using the $30 gift certificate?

Answer options with 5 options
A.
8 x plus 4.5 y is less than or equal to 30

B.
4.5 x plus 8 y is less than or equal to 30

C.
30 x plus 4.5 y is greater than or equal to 8

D.
30 x plus 4.5 y is less than or equal to 8

E.
8 x plus 30 y is greater than or equal to 4.5

Answer 1

To find the right inequality that represents the total cost of adult and children's tickets in relation to the $30 gift certificate, we need to set up the situation.

Let:

• \( x \) = number of adult tickets
• \( y \) = number of children's tickets

The cost for adult tickets is \( 8.00x \) and the cost for children's tickets is \( 4.50y \).

The total cost must be less than or equal to $30, so we can write the inequality as:

\[ 8x + 4.5y \leq 30 \]

Now let's match this with the provided answer options.

A. \( 8x + 4.5y \leq 30 \) (This matches our inequality)

B. \( 4.5x + 8y \leq 30 \) (This does not match)

C. \( 30x + 4.5y \geq 8 \) (This does not match)

D. \( 30x + 4.5y \leq 8 \) (This does not match)

E. \( 8x + 30y \geq 4.5 \) (This does not match)

Thus, the correct answer is:

A. \( 8x + 4.5y \leq 30 \)