Question

At a zoo, the price of 4 adult tickets and 6 child tickets is $77. The price of 6 adult tickets and 4 child tickets is $83. What is the ticket price for one adult and for one child?

Answer 1

The cost of 1 adult ticket is $9.5

The cost of 1 child ticket is $6.5

Explanation:

Given :

The price of 4 adult tickets and 6 child tickets is $77.

The price of 6 adult tickets and 4 child tickets is $83.

To Find : he ticket price for one adult and for one child.

Solution :

Let the cost of one ticket of adult be $x

Cost of 4 adult tickets = $4 x

Cost of 6 adult tickets = $6 x

Let the cost of one ticket of child be $y

Cost of 6 child tickets = $6 x

Cost of 4 child tickets = $4 x

Now , we are given that the price of 4 adult tickets and 6 child tickets is $77.

⇒
`4 x+6 y = 77` ---(a)

Also we are given that price of 6 adult tickets and 4 child tickets is $83.

⇒
`6 x+4 y =83` ---(b)

Now solve equation (a) and (b) by substitution method

Substituting value of x from equation (a) in equation (b)

`6((77-6 y)/(4)) +4 y =83`

`(462-36 y)/(4) +4 y =83`

`115.5-9 y +4 y =83`

`115.5-5y =83`

`115.5-83 =5y`

`32.5 =5y`

`(32.5)/(5) =y`

`6.5=y`

Thus, The cost of 1 child ticket is $6.5

To calculate x put y in equation (a)

⇒
`4 x+6 (6.5) = 77`

⇒
`4 x+39 = 77`

⇒
`4 x= 77-39`

⇒
`4 x= 38`

⇒
`(38)/(4) =x`

⇒
`x= 9.5`

Thus the cost of 1 adult ticket is $9.5