Question

Which problem situation could the inequality below represent? 30 + 6x < $80 Select one: O A. 30 students attend a parade and the cost to get in is $6 each. How many can get in if they have $80 to spend? B. Mark has at most $80 he can spend shopping. He wants a pair of shoes that cost $30 and wants to spend the rest on tee shirts that cost $6 each. How many tee shirts can he buy? O C. The band is having a fund raiser and they want to earn a minimum of $80. They received a $30 dollar donation and will sell tickets to a concert for $6 each. How many tickets must they sell? O D. John needs to make exactly $80 working today. He gets paid $30 per day and $6 for every tree he cuts down. How many trees must he cut down today?

Answer 1

Analyze each option to obtain mathematical expressions that model the situation. Then, identify which of them matches the given inequality.

A)

Since the cost to get in is $6 each student, for a number x of students, the cost will be 6x. If they have $80 to spend, then the maximum number of students will be the greatest whole number such that:

`6x<80`

B)

Since Mark will buy a pair of shoes, he will spend at least $30. For a given number x of shirts, he will spend 6x more. In total, he will spend 30+6x to buy x shirts and a pair of shoes. This quantity should be lower than $80:

`30+6x<80`

C)

Since the band will earn $6 for each ticket, their total earnings for x tickets would be 6x. Additionaly, they already have $30 and they want to earn a minimum of $80, so the number of tickets must satisfy the condition:

`80<30+6x`

D)

If John works one day and cuts x trees, he will earn 30+6x. If this quantity has to be exactly equal to $80, then x must satisfy the condition:

`30+6x=80`

Since the only option that uses the inequality 30+6x<80 is B), that's the only possible answer.