The admission fee at a small fare is $1.50 for children and $4.00 for adults. On a certain day ,2200 people entered the fair and $5050 was collected.How
many children and how many adults attended. This needs to be written in a linear equation.

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absor201 absor201 · Answer 1 · 2020-01-15T15:38:58+01:00

1500 child tickets and 700 adult tickets were sold.

Step-by-step explanation:

Given,

Cost of child ticket = $1.50

Cost of adult ticket = $4.00

Number of people entered = 2200

Revenue generated = $5050

Let,

x represent the number of children tickets sold.

y represent the number of adults tickets sold.

According to given statement;

x+y=2200 Eqn 1

1.50x+4.00y=5050 Eqn 2

Multiply Eqn 1 by 1.50

[tex]1.50(x+y=2200)\\1.50x+1.50y=3300\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](1.50x+4.00y)-(1.50x+1.50y)=5050-3300\\1.50x+4.00y-1.50x-1.50y=1750\\2.50y=1750[/tex]

Dividing both sides by 2.50

[tex]\frac{2.50y}{2.50}=\frac{1750}{2.50}\\y=700[/tex]

Putting y=700 in Eqn 1

[tex]x+700=2200\\x=2200-700\\x=1500[/tex]

1500 child tickets and 700 adult tickets were sold.

Keywords: linear equation, elimination method

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