Two different families bought general admission tickets for a reno aces baseball game. One family paid $45 for 5 adults and 2 children. The other family paid $39 for 2 adults and 5 children. Write a system to represent the problem and solve

System is as below:

5x + 2y = 45 (equation 1)

2x + 5y = 39 (equation 2)

Solving the system results in:

x = 7

y = 5

Step-by-step explanation:

Given dа ta:

One family paid $45 for 5 adults and 2 children.

The other family paid $39 for 2 adults and 5 children.

Let the price for an adult be x

Let the price for a child be y

The system of equation will be

5x + 2y = 45 (equation 1)

2x + 5y = 39 (equation 2)

Solving the equation using elimination method

Eliminate x by the coefficients of x in equation 1 and 2

5x + 2y = 45 (Multiply the whole equation by 2)

2x + 5y = 39 (Multiply the whole equation by 5)

10x + 4y = 90

10x + 25y = 195 (Subtract the equation)

0x + (-21y) = (-105)

-21y = - 105

y = 5

Substituting y into equation 1

5x + 2y = 45

5x + 2 (5) = 45

5x + 10 = 45

5x = 45-10

5x = 35

x = 7