Question

The admission fee is $1.50 for children and $4.00 for adults. If 2700 people enter and $7800 is collected how many children and how many adults attended.

Answer 1

Number of children attended is 1200 and number of adults attended is 1500

Solution:

Given that,

Admission fee for each children = $ 1.50

Admission fee for each adult = $ 4.00

Let "c" be the number of children attended

Let "a" be the number of adults attended

Given that 2700 people enter and $7800 is collected

Number of children attended + number of adults attended = 2700

c + a = 2700 -------- eqn 1

Also given that $7800 is collected

Number of children attended x Admission fee for each children + number of adults attended x Admission fee for each adult = 7800

`c * 1.50 + a * 4 = 7800`

1.5c + 4a = 7800 -------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "c"

From eqn1,

a = 2700 - c ----- eqn 3

Substitute eqn 3 in eqn 2

1.5c + 4(2700 - c) = 7800

1.5c + 10800 - 4c = 7800

-2.5c = -3000

c = 1200

Therefore from eqn 3,

a = 2700 - 1200

a = 1500

Therefore number of children attended = c = 1200

number of adults attended = a = 1500