Question

⦁ The cost of a ticket to the circus is $25.00 for children and $50.00 for adults. On a certain day, attendance at the circus is 2,000 and the total gate revenue is $70,000. Write mathematical formulation of the problem, to determine the number of children and adults attended circus on that day.

Answer 1

$\red{\large\underline{\sf{Given- }}}$

The cost of a ticket to the circus is $ 25.00 for children and $ 50.00 for adults.

On a certain day, attendance at the circus is 2,000 and the total gate revenue is $ 70,000.

$\purple{\large\underline{\sf{To\:Find - }}}$

Mathematical formulation of the problem, to determine the number of children and adults attended circus on that day.

$\pink{\large\underline{\sf{Solution-}}}$

Given that,

• The cost of a ticket to the circus is $ 25.00 for children and $ 50.00 for adults.

• On a certain day, attendance at the circus is 2,000 and the total gate revenue is $ 70,000.

Let assume that

• Number of children be x

• Number of adults be y

According to statement

Attendance of the people at circus = 2000

$\rm \implies\:\boxed{\tt{ \: x + y = 2000 \: }}$

According to statement

Cost of ticket for 1 children = $ 25

Cost of ticket for x children = $ 25x

Cost of ticket for 1 adult = $ 50

Cost of ticket for y adults = $ 50y

Since, total revenue is $ 70,000

$\rm :\longmapsto\:25x + 50y = 70000$

$\rm :\longmapsto\:25(x + 2y) = 70000$

$\rm :\longmapsto\:x + 2y = 2800$

$\rm \implies\:\boxed{\tt{ \: x + 2y = 2800 \: }}$

So, Mathematical formulation of the problem

$\red{\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{x \: + \: y \: = \: 2000} \\ \\ &\sf{x \: + \: 2y \: = \: 280} \end{cases}\end{gathered}\end{gathered}}$

Answer 2

Answer:

let the number of children=x

let the number of adults=y

according to the question -

25x+50y=70,000-----(1)

x+y=2000------(2)

after applying elimination method-

25y=20,000

y=800

put value of y in equation (1) we get-

x= 1200

so, number of children=1200

number of adults=800