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
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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