The total cost for a bucket of popcom and 4 movie tickets is . The total cost for the same size bucket of popcom
and 6 movic tickets is . The cost of a bucket of popcorn is . Which equation represcnts the relationship
benween the total cost of the popcorn and movie tickets, and , the number of movie tickets that are purchased?

Ask by Bush Santiago. in the United States

Jan 23,2025

Question

The total cost for a bucket of popcom and 4 movie tickets is . The total cost for the same size bucket of popcom
and 6 movic tickets is . The cost of a bucket of popcorn is . Which equation represcnts the relationship
benween the total cost of the popcorn and movie tickets, and , the number of movie tickets that are purchased?

Ask by Bush Santiago. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To determine the relationship between $$ y $$ (the total cost) and $$ x $$ (the number of movie tickets), let's break down the problem step by step.

1. **Given Information:**
   - Cost of a bucket of popcorn ($$ p $$): \$8
   - Total cost for popcorn and 4 movie tickets: \$56
   - Total cost for popcorn and 6 movie tickets: \$80

2. **Let $$ t $$ be the cost of one movie ticket.**

3. **Set Up the Equations:**
   - From the first scenario:
     $$
     p + 4t = 56
     $$
     Substituting $$ p = 8 $$:
     $$
     8 + 4t = 56 \implies 4t = 48 \implies t = 12
     $$
   - From the second scenario (to verify):
     $$
     p + 6t = 80
     $$
     Substituting $$ p = 8 $$ and $$ t = 12 $$:
     $$
     8 + 6(12) = 8 + 72 = 80 \quad \text{(which matches)}
     $$

4. **Formulate the Equation:**
   - The total cost $$ y $$ is the sum of the cost of popcorn and the cost of movie tickets:
     $$
     y = p + xt
     $$
     Substituting $$ p = 8 $$ and $$ t = 12 $$:
     $$
     y = 8 + 12x
     $$
     Which can also be written as:
     $$
     y = 12x + 8
     $$

**Answer:** $$ y = 12x + 8 $$
The equation representing the relationship is $$ y = 12x + 8 $$.

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