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27 votes
27 votes
Two families go to a zoo.

The Smith family of two adults and three children pay £61.
The Jones family of three adults and five children pay £96.
Work out the cost of an adult ticket and the cost of a child ticket.
In your working, let 'a' stand for an adult ticket and 'c' stand for a child ticket.

User DuSant
by
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1 Answer

21 votes
21 votes

Answer:

child = $9

adult = $17

Explanation:

Two families go to a zoo. The Smith family of two adults and three children pay £61. The Jones family of three adults and five children pay £96. Work out the cost of an adult ticket and the cost of a child ticket. In your working, let 'a' stand for an adult ticket and 'c' stand for a child ticket.

Family 1: 2a + 3c = 61

Family 2: 3a + 5c = 96

solve family 1 in terms of a:

2a + 3c = 61

subtract 3c from both sides:

2a + 3c - 3c = 61 - 3c

2a = 61 - 3c

divide both sides by 2:

2a/2 = (61 - 3c)/2

a = 61/2 - 3/2c

plug [a = 61/2 - 3/2c] into Family 2 equation:

3a + 5c = 96

3(61/2 - 3/2c) + 5c = 96

multiply:

3(61/2 - 3/2c) + 5c = 96

91.5 - 4.5c + 5c = 96

subtract 91.5 from both sides:

91.5 - 4.5c + 5c - 91.5 = 96 = 91.5

- 4.5c + 5c = 4.5

combine left side:

0.5c = 4.5

divide both sides by 0.5:

0.5c/0.5 = 4.5/0.5

c = 9

Now solve for a. We will use Family 1 equation:

2a + 3c = 61 where c = 9

2a + 3(9) = 61

2a + 27 = 61

subtract 27 from both sides:

2a + 27 - 27 = 61 - 27

2a = 34

divide both sides by 2:

2a/2 = 34/2

a = 17

__________________________________________

Let's check out numbers:

where c = 9 and a = 17

Family 1: 2a + 3c = 61

2(17) + 3(9) = 61

34 + 27 = 61

61 = 61

Family 2: 3a + 5c = 96

3(17) + 5(9) = 96

51 + 45 = 96

96 = 96

User Kordonme
by
2.8k points