The Douglas family visits SeaLand and is charged $72.00 for 2 adult and 3 child tickets. The Williams family also visited SeaLand and was charged $78.00 for 1 adult and 5 child tickets. How much would it cost the Lopez family to go to SeaLand if they have 3 adults and 4 children?

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

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step-by-step explanation:

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step-by-step explanation: