Question

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Two families go to a zoo.
The Smith family of two adults and three children pay £66.
The Jones family of three adults and five children pay £105.
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.

Answer 1

Let's solve your system by elimination.

2a + 3c =66 ; 3a + 5c = 105

Multiply the first equation by 5,and multiply the second equation by -3.

5 (2a + 3c = 66)

−3 (3a + 5c = 105)

Becomes:

10a + 15c = 330

−9a − 15c = −315

Add these equations to eliminate c:

a = 15

Now that we've found a let's plug it back in to solve for c.

Write down an original equation:

2a + 3c = 66

Substitute 15 for a in 2a + 3c = 66:

(2)(15) + 3c = 66

3c + 30 = 66 (Simplify both sides of the equation)

3c + 30 −30 = 66 −30 (Add -30 to both sides)

3c = 36

3c3= 363 (Divide both sides by 3)

c = 12

Answer:

a = 15 and c = 12