Question

Abby, Brenda, Celia, Denise, and Elizabeth are going to their town’s annual hayride. Tickets cost $8.00 for people 12 years old and older but only $5.00 for people 11 years old and younger. The total price for their five tickets is $31.00. How many people in the group are 12 years old or older?

A) 2
B) 3
C) 4
D) 5

Answer 1

To find out how many people in the group are 12 years old or older, we can set up a system of equations using the given information. Solving these equations simultaneously, we can find the values of x and y. Therefore, there are 2 people in the group who are 12 years old or older.

Step-by-step explanation:

To find out how many people in the group are 12 years old or older, we can set up a system of equations using the given information. Let's assume that x represents the number of people who are 12 years old or older, and y represents the number of people who are 11 years old or younger. We can then set up the following two equations:

1. x + y = 5 (since there are a total of 5 people in the group)
2. 8x + 5y = 31 (since the total cost of the tickets is $31)

Solving these equations simultaneously, we can find the values of x and y:

1. Multiplying the first equation by 8, we get 8x + 8y = 40
2. Subtracting the second equation from this new equation, we get 8y - 5y = 40 - 31
3. Simplifying, we get 3y = 9
4. Dividing both sides by 3, we get y = 3
5. Substituting this value of y into the first equation, we get x + 3 = 5
6. Subtracting 3 from both sides, we get x = 2

Therefore, there are 2 people in the group who are 12 years old or older.