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 o

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

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Thành Công 4 months 2021-08-18T07:01:07+00:00 1 Answers 0 views 0

Answers ( )

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    2021-08-18T07:02:20+00:00

    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

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