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

Answer 1

Answer: Correct, the system of equations representing the given information is:

• 2x + 3y = 1240 (Total amount collected at the carnival)
  
  
• x = 2y - 10 (Number of food tickets sold is 10 less than twice the number of ride tickets sold)

Now, let's solve the system of equations to find the values of x and y.

Step 1: Use equation 2 to substitute for x in equation 1.

Substitute x = 2y - 10 into equation 1:

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

Step 2: Simplify and solve for y.

4y - 20 + 3y = 1240

7y - 20 = 1240

Step 3: Move the constant term to the other side.

7y = 1240 + 20

7y = 1260

Step 4: Divide by 7 to solve for y.

y = 1260 / 7

y = 180

Step 5: Now that we have the value of y, use equation 2 to find the value of x.

x = 2y - 10

x = 2(180) - 10

x = 360 - 10

x = 350

So, the number of ride tickets sold (y) is 180, and the number of food tickets sold (x) is 350.