**Solutions**

- Let
*x*= amount invested in the corporate bond500,000 –

*x*= amount invested in the treasury bond0.08

*x*= annual interest from the corporate bond0.0525(500,000 –

*x*) = annual interest from the treasury bondCorporate bond interest + Treasury bond interest ≥ 30,000

The administrator should invest at least $136,363.64 in the corporate bond in order to receive at least $30,000 per year in interest payments.

- Let
*x*= number of corn dogs sold per day2

*x*= revenue200 + 0.35

*x*= overhead costs + production costs = total costKelly needs to sell at least 400 corn dogs in order for her daily profit to be at least $460.

- Let
*x*= number of snow cones sold per month1.50

*x*= revenue600 + 0.25

*x*= overhead costs + production costs = total costRevenue > Cost

The owner should sell more than 480 snow cones per month to make a profit.

- Let
*x*= number of tee shirts sold per month18

*x*= revenue1500 + 8

*x*= overhead costs + production costs = total cost18

*x*–(1500 + 8*x*)= profitProfit ≥ 3500

At least 500 tee shirts would need to be sold each month to make a monthly profit of at least $3500.

- Let
*x*= number of daily milesThe $24 option costs 24 + 0.80

*x*per day.The most a customer could drive is 200 miles per day in order for the $24 plan to cost no more than the $40 plan.

- The first 50 hours are free under the $12 plan, so let
*x*represent the number of hours used beyond 50 hours. Each hour beyond 50 costs 0.65*x*.A family would need to use more than 20 hours per month beyond 50 hours (or more than 70 hours per month) in order for the unlimited plan to cost less than the limited hour plan.

- Let
*x*= number of times Sharon uses her skates The cost to rent skates is 3*x*.Sharon would need to use her skates more than 20 times to justify purchasing them instead of renting them.

- Let
*x*= number of kilowatt-hours used per month28 + 0.07

*x*= monthly billThe James family can use no more than 2600 kilowatt-hours per month in order to keep their electricity costs within their budget.

- Let
*x*= amount spent at the store annually 0.05*x*= extra 5% purchase charge per yearA shopper would need to spend at least $800 per year to justify the $40 annual fee.

- Let
*x*= annual sales level0.08

*x*= annual commission15,000 + 0.08

*x*= annual salary plus commissionThe sales clerk would need an annual sales level of $125,000 or more in order for the salary plus commission option to be at least as attractive as the straight salary option.

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

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