Question

in 13 and 14, use the table.

1. higher order thinking james bought a movie ticket and popcorn for $12.20. the movie ticket cost $8.45. use the equation c + $8.45 = $12.20 to find which size popcorn james bought. how much change did james get if he paid with a $20 bill?
2. reasoning kyle bought a movie ticket for $8.45 and a drink for $1.80. he had just enough money remaining to buy a large popcorn. how much money did kyle start with? write an equation to show your reasoning.

cost of popcorns
small $2.85
medium $3.75
large $4.75
extra large $4.85

Explanation:

Problem 13 (James' Popcorn and Change)

Step1: Solve for popcorn cost ($c$)

We have the equation \( c + \$8.45 = \$12.20 \). To find \( c \), subtract \( \$8.45 \) from both sides:
\( c = \$12.20 - \$8.45 = \$3.75 \).

Step2: Identify popcorn size

From the table, the medium popcorn costs \( \$3.75 \), so James bought medium popcorn.

Step3: Calculate change

James paid with a \( \$20 \) bill. Total spent: \( \$12.20 \).
Change = \( \$20 - \$12.20 = \$7.80 \).

Step1: Define variables and costs

Let \( m \) = money Kyle started with.
Costs: ticket (\( \$8.45 \)), drink (\( \$1.80 \)), large popcorn (\( \$4.75 \)).

Step2: Write the equation

Total spent = ticket + drink + popcorn. Since he had just enough to buy the popcorn, his starting money equals total spent:
\( m = \$8.45 + \$1.80 + \$4.75 \).

Step3: Solve the equation

Calculate total: \( \$8.45 + \$1.80 = \$10.25 \); \( \$10.25 + \$4.75 = \$15.00 \).

Answer:

• Popcorn size: Medium
• Change: \(\$7.80\)

Problem 14 (Kyle's Starting Money)