Question

A local drama production sold tickets for a play. Adult tickets sold for $10 each and child tickets sold for $5

each. During the weekend, they collected $1750 from ticket sales. There was a total of 225 tickets sold.

a) Write an equation to represent the total cost and another equation to represent the total people.

b) How many of each ticket was sold?

c) Verify your solution using the system of equations.​

Answer 1

a) The total cost will therefore be :

$10x + $5y = $1750

(ii) The total number of people will therefore be written as:

x + y = 225

(b) Adult ticket = 125 , children = 100

Explanation:

Let x represent the total number of adult and let y represent the total number of children.

The cost of ticket for 1 adult = $10 , therefore:

The cost ticket for x adults = $10x

The cost of ticket for a child = $5 , therefore :

the cost of ticket for y children = $5y

This means that

(a) The total cost will therefore be :

$10x + $5y = $1750

(ii) The total number of people will therefore be written as:

x + y = 225

(b) combining the two equations together , we will have

10x + 5y = 1750 ............................... equation 1

x + y = 225 ....................................... equation 2

solving the resulting linear equations by elimination method, from equation 2, make x the subject of formula, equation 2 then becomes

x = 225 - y ....................... equation 3

substitute x = 225 - y into equation 1 , equation 1 then becomes

10 ( 225 - y ) + 5y = 1750

expanding , we have

2250 - 10y + 5y = 1750

2250 - 5y = 1750

2250 - 1750 = 5y

500 = 5y

divide through by 5

y = 100

substitute y = 100 into equation 3 to find the value of x

x = 225 - 100

x = 125

Therefore : 125 adults ticket were sold and 100 children tickets were sold

(c) check : we will substitute the number of each tickets sold into the equation

10x + 5y = 1750

x = 125 , y = 100

10 ( 125 ) + 5 (100)

1250 + 500

= 1750

Also

x + y = 225

125 + 100 = 225