Question

At an amusment park, the cost for an adult admission is a, and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95. All ticket prices include tax.

Part A / Write a system of equations in terms of a and c, that models this situation.

Part B / Use your systems of equations to determine the exact cost of each type of ticket algebraically

Part C / Determine the cost for a group of four that includes three children

Answer 1

4A +2C=325.94
2A + 3C = 256.95

Make the B’s Match ( C in this case)
First row all multiply by 3
Second row all multiple by 2

12A+6C = 977.82
4A+ 6C = 513.90

Now do the equation

8A = 463.92
Now divide both by 8

A = 57.99

Now use one equation to fine C ( cost of children)

4(57.99)+2C = 325.94

231.96 + 2C = 325.94

2C = 325.94 - 231.96
2C = 93.98
Divide by 2

C = 46.99


Part c

1A +3C=
1(57.99) + 3(46.99)= the cost
57.99 + 140.97= the cost

198.96= the cost