Question

The cost for 5 adults and 3 children to attend a show is $210. ( /5)
For 2 adults and 5 children the cost is $160.
Form a pair of simultaneous linear equations and solve them to find the cost of:
i. an adult ticket
ii. a child ticket

Answer 1

Answer: i. Cost of adult ticket = $ 30

ii.  Cost of child ticket = $20

Step-by-step explanation:

Define variables:

Let x= cost of 1 adult tickets , y= cost of 1 child tickets.

Form linear equations:

5x+3y = 210      (i)

2x+5y= 160  (ii)

Multiply (i) by 2 and (ii) by 5

10x +6y = 420       (iii)

10x+25y = 800        (iv)

Eliminate (iii) from (iv)

19y = 380

⇒ y= 20

Put this in (i)

$5x+3(20)=210\Rightarrow\ 5x+60 = 210\\\\\Rightarrow\ 5x=150\\\\\Rightarrow\ x=30$

Hence, Cost of adult ticket = $ 30 and Cost of child ticket = $20