Question

select the correct answer.
cindy took her five grandchildren to the movies, where she offered to buy all of them popcorn and candy. a popcorn bag costs $4.00, and a box of candy costs $2.50. cindy ended up spending $35.00 and purchasing one more box of candy than bags of popcorn.
use a system of equations to model the situation above, and determine which of the following is a possible description of cindy’s purchase

a. 5 bags of popcorn, 6 boxes of candy
b. 4 bags of popcorn, 5 boxes of candy
c. 6 bags of popcorn, 5 boxes of candy
d. 5 bags of popcorn, 4 boxes of candy

Explanation:

Step1: Define variables

Let \( x \) be the number of popcorn bags and \( y \) be the number of candy boxes.

Step2: Set up equations

From "one more box of candy than bags of popcorn", we get \( y = x + 1 \).
From the cost: \( 4x + 2.5y = 35 \).

Step3: Substitute \( y \) into cost equation

Substitute \( y = x + 1 \) into \( 4x + 2.5y = 35 \):
\( 4x + 2.5(x + 1) = 35 \)
\( 4x + 2.5x + 2.5 = 35 \)
\( 6.5x = 32.5 \)
\( x = 5 \)

Step4: Find \( y \)

\( y = x + 1 = 5 + 1 = 6 \)

Answer:

A. 5 bags of popcorn, 6 boxes of candy