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
