# Water Park

As the bookkeeper for the local water park, I noticed that on Saturday there were 4,296 children and 2,143 adults tickets sold for a total of: \$98,718.00.

However, on Sunday, there were 5,146 children and 2,807 adults and the totals were \$122,570.00

How much are the adults tickets and how much are the children’s tickets?

### 3 guesses to Water Park

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• Chini

Children Ticket – 14

• Dude

You’re right, Chini.

Adult’s tickets were \$18 and children’s were \$14.

This is easily solved using a common method for solving simultaneous equations.
First construct two algebraic equations, where C is the number of children, and A is the number of adults:

4296C + 2143A = 98718 [1]
5146C + 2807A = 122570 [2]

To make the number in front of C the same on both we multiple [1] by 5146 and [2] by 4296 to give:

22107216C + 11027878A = 508002828 [3]
22107216C + 12058872A = 526560720 [4]

Now we can do [4] – [3] to give:

1030994A = 18557892

Divide throughout by 1030994 so that:

A = 18

Substituting A = 18 in [1] will give:

4296C + 2143 x 18 = 98718
4296C + 38574 = 98718
4296C = 60144

C = 14

You are today’s winner.