solving compound inequalities (word problems)

Question

Write the iniequality and use it to solve the problem:

 

At the San Diego Zoo, you can either pay $22.75 for the entrance fee or $71 for the yearly pass, which entitles you to unlimited admission. At most, how many times can you enter the zoo for the $22.75 entrance fee before spending more than the cost of a yearly membership?

Virena’s Scout Troop is trying to raise at least $650 this spring. How many boxes of cookies must they sell at $4.50 per box in order to reach their goal?

Answer 1

1.

 

This does not require the use of compound inequality concept.

 

Let the most number of times you enter the zoo = ×

 

The following inequality can be used to find the most number of times:

 

22.75× ≤ 71

 

         × ≤ 71/22.75

 

         × ≤ 3.12

 

Therefore the most number of times you can enter the zoo to pay the entrance fee before spending more than the yearly fee of $71 = 3 times.

 

Note that your answer cannot be decimal. It has to be an integer. It cannot be 4 because you will end up spending more than $71.

 

2.

 

Let the number of boxes required = ×

 

4.75× ≥ 650

 

       × ≥ 650/4.75

 

       × ≥ 136.84

 

Therefore, the scout troop must sell at least 137 boxes of cookies to reach their goal.