Question

Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets.

Answer 1

Complete Question

Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. Could they take 9 children and 4 adults to both shows? Show your work. A yes or no answer is not sufficient for credit.

Answer:

Yes it is  possible to take the  9 children and 4 adults to both shows

Step-by-step explanation:

From the question we are told that

    The  cost of the Matinee tickets for a child is  z =  $4

    The  cost of the Matinee tickets for an adult is  a  = $ 4

     The cost of the Evening tickets for  a child is  k =  $6

      The cost of the Evening tickets for an adult is  b =  $8    

      The  maximum amount to be spent on Matinee tickets is  m = $80

       The maximum amount to be spent on Evening tickets is  e =  $100

       The  number of child to be taken to the movies is  n  = 9

        The number of adults to be taken to the movies is  j  =  4

Now the total amount of money that would be spent on Matinee tickets is  mathematically evaluated as      

           $t = 4 n + 4 j$

substituting values

           $t = 4 * 9 + 4* 4$

           $t = 52$

Now the total amount of money that would be spent on  Evening ticket is mathematically evaluated as      

      $T = 6n + 8j$

substituting values

     $T = 6(9) + 8(4)$

    $T = 86$

This implies that it is possible to take 9 children and 4 adults to both shows

given that

      $t \le m$

i.e  $56  $\le$$ 80

and  

      $T \le e$

i.e   $ 86 $\le$ $ 100