Question

penny purchases 100 tickets for her youth services group to attend a waterpark. Child admissions are 14 dollars each while adult admissions are 19 dollars each. If the total cost for the tickets was 1470 dollars, how many of each type of ticket did she purchase

Answer 1

Penny purchased 86 child admissions and 14 adult admissions.

Step-by-step explanation:

Let's use an algebraic approach to solve this problem. Let x represent the number of child admissions and y represent the number of adult admissions. We can set up two equations based on the given information:

Equation 1: 14x + 19y = 1470 (total cost of tickets)

Equation 2: x + y = 100 (total number of tickets)

To solve the system of equations, we can use the substitution method or elimination method. Let's use the elimination method:

1. Multiply Equation 2 by 14: 14x + 14y = 1400
2. Subtract Equation 1 from the resulting equation: 14x + 14y - (14x + 19y) = 1400 - 1470
3. Simplify: -5y = -70
4. Divide both sides by -5: y = 14
5. Substitute the value of y into Equation 2: x + 14 = 100
6. Solve for x: x = 100 - 14 = 86

Therefore, Penny purchased 86 child admissions and 14 adult admissions.

Answer 2

Penny purchased 70 child tickets and 20 adult tickets.

Step-by-step explanation:

Let's assume that Penny purchased x child tickets and y adult tickets.

The cost of each child ticket is $14, so the total cost of child tickets will be 14x dollars.

The cost of each adult ticket is $19, so the total cost of adult tickets will be 19y dollars.

According to the given information, the total cost of all the tickets is $1470, so we can write the equation:

14x + 19y = 1470

Now, we need to solve this equation to find the values of x and y.

Since we don't have any further information, there are multiple possible solutions for this equation. One possible solution could be x = 70 and y = 20.

Therefore, Penny purchased 70 child tickets and 20 adult tickets.