Question

The admission fee at an amusement park is $20 for children and $35 for adults. On a certain day, 390 people entered the park, and the admission fees collected totaled $10650. How many children and how many adults were admitted? NUMBER OF CHILDREN= ? NUMBER OF ADULTS= ?

Answer 1

Children = 200

Adults = 190

Explanation:

Children = x

Adults = y

x + y = 390

x = 390 - y..............(1)

20x + 35y = 10650

Substituting

20(390-y) + 35y = 10650

y = 190

x = 390 - 190 = 200

Answer 2

Explanation:

Number of children = c

Number of adults = a

Total people = 390

a + c = 390 ------------------ (I)

Admission fee for 'c' children = 20 * c = 20c

Admission fee for 'a' adult = 35 * a = 35a

Total amount = $ 10650

35a + 20c = 10650 -------------(II)

Multiply equation (I) by (-20)

(I)*(-20) -20a - 20c = - 7800

(II) 35a + 20c = 10650 { Now add and so 'c' will be eliminated}

15a = 2850

a = 2850/15

a = 190

Plug in a = 190 in equation (I)

190 + c = 390

c = 390 - 190

c = 200

Number of children = 200

Number of adults = 190