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

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