Question

at a carnival, food tickets cost $2 each and ride tickets cost $3 each. a total of $1,240 was collected at the carnival. the number of food tickets sold was 10 less than twice the number of ride tickets sold.

the system of equations represents \\(x\\), the number of food tickets sold, and \\(y\\), the number of ride tickets sold.

\\2x + 3y = 1240\\
\\x = 2y - 10\\

how many of each type of ticket were sold?

180 food tickets and 293 ride tickets
180 food tickets and 350 ride tickets
293 food tickets and 180 ride tickets
350 food tickets and 180 ride tickets

Explanation:

Set up the system of equations

Using the Systems of Linear Equations knowledge point
We are given the system of equations representing the ticket sales:

$$
LATEXBLOCK0
$$

where:

• \(x\) is the number of food tickets sold.
• \(y\) is the number of ride tickets sold.

Substitute Equation 2 into Equation 1

Using the Systems of Linear Equations knowledge point

$$ 2(2y - 10) + 3y = 1240 $$

Solve for y

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Solve for x

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK2
$$

Verify the solution

Using the Systems of Linear Equations knowledge point

$$
LATEXBLOCK3
$$

Thus, 350 food tickets and 180 ride tickets were sold.

Answer:

• 180 food tickets and 293 ride tickets
• 180 food tickets and 350 ride tickets
• 293 food tickets and 180 ride tickets
• 350 food tickets and 180 ride tickets (Correct answer)