Double Inequalities Help (page 2)

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By — McGraw-Hill Professional
Updated on Sep 26, 2011

Double Inequality Word Problems

The applied problems in this section are similar to problems earlier in this chapter. The only difference is that you are given a range for one value and you are asked to find the range for the other.


Example 1:

A high school student earns $8 per hour in her summer job. She hopes to earn between $120 and $200 per week. What range of hours will she need to work so that her pay is in this range?

Let x represent the number of hours worked per week. Represent her weekly pay by p = 8 x . The student wants 120 ≤ p ≤ 200. The inequality to solve is 120 ≤ 8 x ≤ 200.

Double Inequalities

The student would need to work between 15 and 25 hours per week for her pay to range from $120 to $200 per week.

Example 2:

A manufacturing plant produces pencils. It has monthly overhead costs of $60,000. Each gross (144) of pencils costs $3.60 to manufacture. The company wants to keep total costs between $96,000 and $150,000 per month. How many gross of pencils should the plant produce to keep its costs in this range?

Let x represent the number of gross of pencils manufactured monthly. Production cost is represented by 3.60 x . Represent the total cost by c = 60,000 + 3.60 x . The manufacturer wants 96,000 ≤ c ≤ 150,000. The inequality to be solved is 96,000 ≤ 60,000 + 3.60 x ≤ 150,000.

Double Inequalities

The manufacturing plant should produce between 10,000 and 25,000 gross per month to keep its monthly costs between $96,000 and $150,000.

Find practice problems and solutions at Double Inequalities Practice Problems - Set 4.

More practice problems for this concept can be found at: Algebra Linear Inequalities Practice Test.

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