Question

The Cooper family, consisting of 6 children and 2 adults, goes to the movies and pays a total of $86. The Griffen birthday party, consisting of 10 children and 3 adults, pays a total of $139 for tickets. Let x = the cost of a child ticket and y = the cost of an adult ticket. How much does a child's ticket cost and how much does an adult ticket cost?

Answer 1

Answer: The cost of child's ticket = $10

The cost of adult ticket = $ 13

Step-by-step explanation:

Let x be the cost of a child ticket and y be the cost of an adult ticket.

Then According to the question, we have

$6x+2y=86..........................(1)\\\\10x+3y=139.......................(2)$

Multiply equation (1) by 3 and equation (2) by 2, then we have

$18x+6y=258.......................(1)\\\\20x+6y=278...........................(2)$

Subtract equation (1) from equation (2), we have

$2x=20\\\\\Rightarrow\ x=10$

Substitute the value of x in equation (1), we get

$60+2y=86\\\\\Rightarrow\ 2y=26\\\\\Rightarrow\ y=13$

Hence, the cost of child's ticket = $10

The cost of adult ticket = $ 13