Question

a matinee ticket costs $6 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who saw a movie was 35, and the total money collected was $70. which of the following options represents the number of adults who saw a movie that day, and the pair of equations that can be solved to find the numbers?

Answer 1

The number of adults who saw a movie that day is 7

and

the pair of equations that can be solved to find the numbers is

6x+y = 70

x + y = 35

Explanation:

Let the total no. of adults who saw the move be x

Let the total no. of child who saw the move be y

Given that the total number of adults (a) and children (c) who saw a movie was 35

thus. x + y = 35

cost of ticket for 1 adult = $6

cost of ticket for 1*x adult = $6*x = $6x

cost of ticket for x adult = $6x

cost of ticket for 1 child = $1

cost of ticket for 1*y child = $1*y = $y

cost of ticket for y child = $y

Total cost for x adult and y child = $(6x+y) _______(2)

Given that he total money collected was $70

Thus, we have two equations

6x+y = 70 -------(1)

x + y = 35

y = 35 - x (using this value of y in equation 1 we have)

6x + 35 - x = 70

=> 5x = 70 -35 = 35

=> x = 35/5 = 7

The number of adults who saw a movie that day is 7

and

the pair of equations that can be solved to find the numbers is

6x+y = 70

x + y = 35