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 child ticket is $6.5 and the cost of 1 adult ticket is $9.5

Explanation:

Given that:

the price of 4 adult tickets & 6 child tickets = $77

the price of 6 adult tickets & 4 child tickets = 83

then the price of 1 adult ticket and 1 child ticket will be:

Let assume that the cost of 1 adult ticket to be $p

Then;

the cost of 4 adult ticket = $4p

Similarly, the cost of 6 adult ticket = $6p

However, assuming that the cost of 1 child ticket is $q

Then;

the cost of 6 child ticket = $6q

the cost of 4 child ticket = $4q

∴

We can express them with their given prices that:

4p + 6q = 77 --- (1)

6p + 4q = 83 --- (2)

From equation (1), let 4p = 77 - 6q

Then;
`p = (77 - 6q)/(4)`

replace the value of p into equation (2)

∴

`6 \Big ( ( 77 - 6q )/(4)\Big) + 4q = 83`

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

`115.5 - 9q + 4q = 83 \\ \\ 115.5 -5q= 83 \\ \\ 115.5 - 83 = 5q \\ \\ 32.5 = 5q`

`q= (32.5)/(5)`

q = 6.5

Since q = 6.5, then using equation (1)

4p + 6(6.5) = 77

4p +39 = 77

4p = 77 -39

4p = 38

p = 38/4

p = 9.5

Thus, the cost of 1 child ticket is $6.5 and the cost of 1 adult ticket is $9.5