Question

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

Answer 1

Answer:

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

Step-by-step 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