Answer:
the cost of 1 child ticket is $6.5 and the cost of 1 adult ticket is $9.5
Step-by-step 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; [tex]p = \dfrac{77 - 6q}{4}[/tex]
replace the value of p into equation (2)
∴
[tex]6 \Big ( \dfrac{ 77 - 6q }{4}\Big) + 4q = 83[/tex]
[tex]\dfrac{462 - 36q}{4}+ 4q = 83[/tex]
[tex]115.5 - 9q + 4q = 83 \\ \\ 115.5 -5q= 83 \\ \\ 115.5 - 83 = 5q \\ \\ 32.5 = 5q[/tex]
[tex]q= \dfrac{32.5}{5}[/tex]
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
