Question

What is the equation for the situation? [The number of pizza meals sold by the concession stand was three times the number of hot dog meals. If the pizza meal cost $4, the hot dog meal cost $2, and the total revenue from the meals was $658, how many of each meal was sold?] 1 point

Answer 1

164.5

Step-by-step explanation: just sat it was mental math

Answer 2

The equation representing the situation is
`\(3x + x = 658\),` where
`\(x\)` is the number of hot dog meals sold. This equation captures the information that the number of pizza meals sold was three times the number of hot dog meals, and the total revenue from the meals amounted to $658.

Step-by-step explanation:

Let's denote
`\(x\)` as the number of hot dog meals sold. Given that the number of pizza meals sold was three times the number of hot dog meals, the number of pizza meals sold is
`\(3x\).` The total revenue from hot dog meals is
`\(2x\)` (as each hot dog meal costs $2), and the total revenue from pizza meals is
`\(4 * 3x = 12x\) (as each pizza meal costs $4).`

The total revenue from both types of meals is the sum of the revenues from hot dog and pizza meals, expressed as
`\(2x + 12x = 14x\)` . According to the problem, the total revenue is $658. Therefore, the equation representing the situation is
`\(14x = 658\).`

To find the value of
`\(x\),` we solve for
`\(x\)` by dividing both sides of the equation by 14:
`\(x = (658)/(14) = 47\).`Thus, the number of hot dog meals sold is 47, and the number of pizza meals sold is
`\(3 * 47 = 141\),` confirming that the number of pizza meals was indeed three times the number of hot dog meals, and the total revenue adds up to $658.

This detailed calculation ensures a clear understanding of the solution to the given problem.