Respuesta :
Answer:
The cost of 1 adult ticket is $9.5
The cost of 1 child ticket is $6.5
Step-by-step 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.
⇒[tex]4 x+6 y = 77[/tex] ---(a)
Also we are given that price of 6 adult tickets and 4 child tickets is $83.
⇒[tex]6 x+4 y =83[/tex] ---(b)
Now solve equation (a) and (b) by substitution method
Substituting value of x from equation (a) in equation (b)
[tex]6(\frac{77-6 y}{4}) +4 y =83[/tex]
[tex]\frac{462-36 y}{4} +4 y =83[/tex]
[tex]115.5-9 y +4 y =83[/tex]
[tex]115.5-5y =83[/tex]
[tex]115.5-83 =5y[/tex]
[tex]32.5 =5y[/tex]
[tex]\frac{32.5}{5} =y[/tex]
[tex]6.5=y[/tex]
Thus, The cost of 1 child ticket is $6.5
To calculate x put y in equation (a)
⇒[tex]4 x+6 (6.5) = 77[/tex]
⇒[tex]4 x+39 = 77[/tex]
⇒[tex]4 x= 77-39 [/tex]
⇒[tex]4 x= 38[/tex]
⇒[tex]\frac{38}{4} =x[/tex]
⇒[tex] x= 9.5[/tex]
Thus the cost of 1 adult ticket is $9.5
