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. Let c represent the number of children they take to both shows and let a represent the number of adults they take to both shows. Write a system of inequalities to model this situation.

Answer 1

Let the number of children taken to the movies = x

Let the number of adults taken to the movies = y

Lets talk about Matinee tickets first:

so 4$ per child/adult

4x + 4y
`\leq` 80 (since the budget is 80$, we can spend 80$ , hence the less- than or equal-to)

4(x+y)
`\leq` 80

x + y
`\leq` 40

So, for the matinee show, the sum of number of children and adults should be less than or equal to 40

Lets talk about the Evening show:

so 6$/child and 8$/adult

6x + 8y
`\leq` 100

2(3x + 4y)
`\leq` 100

3x + 4y
`\leq` 50

So, for the Evening show, the sum of 3 times the number of children and 4 times the number of adults should not exceed 50