Question

Theater tickets for 8 people coast a total of $19.50. if a childs ticket cost $1.50 and an adults ticket cost $3.00, how many of these tickets were bought for adults

Answer 1

Answer:

The number of tickets bought for adults  is 4.

Step-by-step explanation:

let us assume the number of tickets bought for children = x

And, the number of tickets bought for adults  = y

Total number of tickets purchased = 8

⇒Total Number of tickets = Number of ticket bought for {Adults + Children}

or, x + y = 8  .... (1)

  Now, cost of 1 children ticket = $1.50

⇒The cost of x children tickets  = x ( Cost of 1 ticket) = x ($1.50) = 1.50 x

 And, cost of 1 adult ticket = $3

⇒The cost of y adult tickets  = y ( Cost of 1 ticket) = y ($3) = 3y

So,total amount spent on the tickets  =1.5 x  + 3y

According to the question:

x + y = 8  .... (1)

1.5 x  + 3y  = 19.50  .....  (2)

To solve the given system, substitute the value of y = 8 - x from (1) in (2)

We get  1.5 x  + 3y = 19.50 ⇒  1.5 x  + 3(8-x )  = 19.50

or, 1.5 x + 24 - 3x = 19.50

or, -1.5 x = 19.50 - 25.5

or, -1.5 x = 6   ⇒ x = 6/1.5 = 4

⇒ x = 4  ⇒ y = 8 - x = 8 - 4 = 4

or, x = 4, y = 4

Hence, the number of tickets bought for adults  is y  = 4.

Answer 2

Answer:

5 adults 3 children

Step-by-step explanation:

WITH LOGIC:

The price for children is half of the price of adults

We could start thinking of 4 adults and 4 children

But  total for  4 adults = $12   and total for 4 children( $6)

So the the total for 8 people  is $18 (we still need to reach  until $19.5)

We know that the number of children should be odd number (the total cost has decimals) so we know that 4 children is not an answer.

It should be 8 people in total

So since 4 adults ,4 children is not working

It is either 5 children and 3 adults  or 5 adults and 3 children

So the answer is 5 adults and 3 children

5*3=15                              

3*1.5= 4.5                        

15+4.5=19.5

    WITH EQUATION

a= adult    c=  child

a+c = 8           c=(8-a)

3a + 1.5(8-a) = 19.5

3a +12 - 1.5a = 19.5

1.5a=7.5

a=5

c=(8-5) c=3