Question

Which system of equations can be used to solve the following problem. Each child ticket for a ride costs $2.00, while each adult ticket costs $6.00. If the ride collected a total of $148, and 38 tickets were sold, how many of each type ticket were sold? Let c be the number of child tickets and a be the number of adult tickets.

Answer 1

Answer:

The number of child tickets is 20 and the number of adult ticket is 18.

Step-by-step explanation:

 Let  'c' be the number of child tickets and 'a' be the number of adult tickets.

According to question,

Each child ticket for a ride costs $2.00, while each adult ticket costs $6.00

Total cost of child ticket = 2 × number of child rides

                                            = 2c

Total cost of adult ticket = 6 × number of adult rides

                                            =  6a

then, the ride collected a total of $148

This can be shown mathematically as,

2c + 6a  = 148  

Also given total 38 tickets were sold that is

c + a = 38    

Thus, the system of equation becomes,

2c + 6a  = 148  .........(1)

and c + a = 38   .......(2)

Solving system using Elimination method,

Multiply equation ( 2) by 6 , we get,

6c + 6a = 228 .........(3)

Now subtract (2) from (3), we get,

⇒ 6c + 6a -( 2c + 6a) = 228 - 148

⇒ 6c + 6a - 2c -6a  = 228 - 148

⇒ 6c - 2c = 80

⇒ 4c = 80

⇒ c = 20

Substitute c = 20 in (2) , to solve for a , we get

c + a = 38 ⇒ 20 + a = 38 ⇒ a = 38 -20 ⇒  a = 18

Thus, the number of child tickets is 20 and the number of adult ticket is 18.

Answer 2

ANSWER
a) The system of equation is

$a + c = 38$
and

$2c + 6a = 148$

b) 18 child tickets and 20 adult tickets were sold.



EXPLANATION

Let c be the number of child tickets and a be the number of adult tickets.


Since each child ticket costs $2.00, if

$c$
number of child tickets were sold, the cost is
$2c


Also, if

$a$
number of adult tickets will cost $6a


If the ride collected a total of $148, then we can write the equation,

$2c + 6a = 148...eqn(1)$

A total of 38 tickets were sold. This gives us,

$a + c = 38...eqn(2)$


Divide equation (1) by 2 to get,


$c + 3a = 74...eqn(3)$


Equation (3) minus equation (2) gives,

$2a = 36$


$a = 18$


$c = 38 - 18 = 20$