Answer:
It would cost the Lopez family $102.00 to go to Sealand
Step-by-step explanation:
Assume that the cost of each adult ticket is $x and the cost of each child ticket is $y
∵ The adult's ticket costs $x
∵ The child's ticket costs $y
∵ The Douglas family is charged $72.00 for 2 adult and 3 child tickets
∴ 2x + 3y = 72 ⇒ (1)
∵ The Williams family was charged $78.00 for 1 adult and 5 child tickets
∴ x + 5y = 78 ⇒ (2)
Let us solve the system of equations to find x and y
→ Multiply equation (2) by -2 to make the coefficients of x equal in
values and different in signs
∵ -2(x) + -2(5y) = -2(78)
∴ -2x + -10y = -156 ⇒ (3)
→ Add equations (1) and (3) to eliminate x
∵ (2x + -2x) + (3y + -10y) = (72 + -156)
∴ -7y = -84
→ Divide both sides by -7 to find y
∴ y = 12
→ Substitute the value of y in equation (1) or (2) to find x
∵ x + 5(12) = 78
∴ x + 60 = 78
→ Subtract 60 from both sides
∴ x + 60 - 60 = 78 - 60
∴ x = 18
∴ The cost of each adult ticket is $18 and the cost of each child ticket
is $12
∵ Lopez family has 3 adults and 4 children
∴ The cost of the tickets = 3(18) + 4(12) = 54 + 48
∴ The cost of the tickets = 3(18) + 4(12) = 102
∴ It would cost the Lopez family $102.00 to go to Sealand
