Question

two families go to a theatre. the smith family three adults and four children pays £67. the jones family five adults and six children pays £106.work out the price of an adult and child ticket, let a stand for adults and c stand for child

Answer 1

1.)    5 (3a + 4c = 67)  
2.)    -3 (5a + 6c = 106)

1.)    15a + 20c = 335
2.)    -15a - 18c = -318
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                     2c = 17
divide both sides by 2
c = £8.5
substitute c for 8.5 to find a

3a + 4 * 8.5 = 67
3a + 34 = 67
subtract 34 from both sides
3a = 33
divide both sides by 3
a = £11

Answer 2

Using a system of equations, the ticket price for adult and child stands are £11 and £8.5 respectively.

Creating the equations :

3a + 4c = 67 - - - (1)

5a + 6c = 106 - - - (2)

Multiply (1) by 5 and (2) by 3 ;

15a + 20c = 335 - - - - (3)

15a + 18c = 318 - - - (4)

Subtract (4) from (3)

2c = 17

c = 17/2 = 8.5

From (1) :

3a + 4(8.5) = 67

3a + 34 = 67

3a = 33

a = 33/3 = 11

Hence, adult stand = £11 and child stand = £8.5

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