Question

At a local concert, the cost for 7 adults and 5 children was $76.00. The cost for 6 adults and 8 children was $80.00. Find how much it costs for an individual adult and how much it costs for an individual child.

a) Adult ticket price = $5.00, Child ticket price = $3.00
b) Adult ticket price = $10.00, Child ticket price = $2.00
c) Adult ticket price = $8.00, Child ticket price = $4.00
d) Adult ticket price = $7.00, Child ticket price = $6.00

Answer 1

After setting up and solving a system of equations based on the given information, the cost for an individual adult ticket is found to be $8.00 and for an individual child ticket $4.00, which corresponds to option c).

Step-by-step explanation:

To find out the cost for an individual adult and child ticket, we need to set up a system of equations based on the information provided.

Let A represent the cost of an adult ticket and C represent the cost of a child ticket. We have two equations from the scenarios provided:

• 7A + 5C = $76.00
• 6A + 8C = $80.00

Multiply the first equation by 6 and the second equation by 7 to eliminate the A variable:

• (6)(7A + 5C) = 6($76.00)
• (7)(6A + 8C) = 7($80.00)

Which simplifies to:

• 42A + 30C = $456.00
• 42A + 56C = $560.00

Subtract the first new equation from the second:

42A + 56C - (42A + 30C) = $560.00 - $456.00

This simplifies to:

26C = $104.00

Divide both sides by 26 to find the cost of one child ticket:

C = $104.00 / 26

C = $4.00

Now plug the value of C back into one of the original equations:

7A + 5($4.00) = $76.00

7A + $20.00 = $76.00

Subtract $20.00 from both sides to solve for A:

7A = $56.00

Divide both sides by 7 to find the cost of one adult ticket:

A = $56.00 / 7

A = $8.00

So, the cost for an individual adult is $8.00 and for a child is $4.00, which corresponds to option c).