Question

(d) Statement one: Two adult tickets and three children tickets cost $43.00

Statement two: One adult ticket and one ticket for a child cost $18.50

(i) Let x represent the cost of an adult ticket and y the cost of a ticket for a child.
Write TWO equations in x and y to represent the information. (2mks)







(ii) Solve the equation to determine the cost of an adult ticket

Answer 1

Two equations can be used to represent the given information. We can solve for the cost of an adult ticket by using elimination method. The cost of an adult ticket is $12.50.

Step-by-step explanation:

(i) Two equations:

1. 2x + 3y = 43 (Equation 1)
2. x + y = 18.50 (Equation 2)

(ii) To solve for the cost of an adult ticket, we can use the method of substitution or elimination. Let's use elimination:

• Multiply Equation 2 by 2 to eliminate x: 2(x + y) = 2(18.50) --> 2x + 2y = 37 (Equation 3)
• Subtract Equation 3 from Equation 1 to eliminate 2x: (2x + 3y) - (2x + 2y) = 43 - 37 --> 3y - 2y = 6 --> y = 6
• Substitute y = 6 into Equation 2 to find x: x + 6 = 18.50 --> x = 18.50 - 6 = 12.50

Therefore, the cost of an adult ticket is $12.50.

Answer 2

The cost of an adult ticket is $12.50

Step-by-step explanation:

The given information are;

The cost of two adult tickets and three children tickets = $43.00

The cost of one adult ticket and one child ticket = $18.50

Whereby the cost of an adult ticket is represented by x and the cost of a child's ticket is represented by y, we get the following two simultaneous equations;

2·x + 3·y = 43.00...(1)

x + y = 18.5...(2)

(ii) Multiplying equation (2) by 2 and subtracting the result from equation (1) gives;

2·x + 3·y - 2×(x + y) = 43 - 2×18.5 = 6

2·x - 2·x + 3·y - 2·y = 0 + y = 6

∴ y = 6

The cost of each the children ticket = $6.00

From equation (2), where y = 6, we get;

x + y = 18.5

∴ x + 6 = 18.5

x = 18.5 - 6 = 12.5

The cost of an adult ticket, x = $12.50.