Heart of Algebra: Linear Inequalities — Quiz 2

Questions in this quiz (10)

1. A worker earns $$9$$ dollars per hour for the first $$8$$ hours and $$12$$ dollars per hour for additional hours. She saves $$80\%$$ of her earnings. What is the minimum number of additional hours $$h$$ she must work to save at least $$216$$ dollars?

   • $$12$$
   • $$16$$
   • $$17$$
   • $$24$$

2. A homeowner pays $$5,200$$ dollars per year for electricity. After installing solar panels costing $$18,000$$, the yearly cost drops to $$2,800$$. Which inequality can be used to find $$t$$, the number of years for the savings to exceed the installation cost?

   • $$18000$$ > $$(5200-2800)t$$
   • $$18000$$ < $$(5200-2800)t$$
   • $$18000$$ < $$5200t-2800$$
   • $$18000$$ > $$2800t$$

3. A company hires interns and managers. Interns earn $$500$$ dollars per week and managers earn $$900$$ dollars per week. The company needs at least $$12$$ employees and can spend at most $$9,600$$ weekly. Let $$x$$ be interns and $$y$$ managers. Which system represents this situation?

   • $$500x+900y\le9600$$$$x+y\ge12$$
   • $$500x+900y\ge9600$$$$x+y\le12$$
   • $$500x+900y\le9600$$$$x+y\le12$$
   • $$500x+900y\ge9600$$$$x+y\ge12$$

4. A school sells at least $$120$$ tickets before an event and at least $$180$$ during the event. Tickets sold during the event cost $$2$$ dollars less than before. If $$x$$ is the price during the event, which inequality represents revenue of at least $$4,800$$ dollars?

   • $$120(x+2)+180x\le4800$$
   • $$120(x+2)+180x\ge4800$$
   • $$120(x-2)+180x\ge4800$$
   • $$120(x-2)+180x\le4800$$

5. A truck can carry at most $$6,000$$ pounds. It already carries a $$300$$-pound machine. Boxes weigh either $$20$$ pounds or $$50$$ pounds. Which inequality represents possible numbers of boxes $$x$$ and $$y$$?

   • $$20x+50y\le5700$$
   • $$20x+50y\ge5700$$
   • $$50x+20y\le6000$$
   • $$50x+20y\ge6000$$

6. A company has a budget of $$12,000$$ dollars to buy laptops for $$60$$ employees. The budget includes $$5\%$$ tax. What is the maximum price per laptop before tax?

   • $$190.48$$
   • $$200.00$$
   • $$209.52$$
   • $$210.00$$

7. $$y\le -x$$ $$y\ge x-2$$Which point is a solution?

   • $$(2,0)$$
   • $$(0,-1)$$
   • $$(1,3)$$
   • $$(-2,3)$$

8. A cleaning service can carry at most $$250$$ pounds. Each vacuum weighs $$12$$ pounds and each mop bucket weighs $$8$$ pounds. The service wants at least twice as many buckets as vacuums. Which system represents this?

   • $$12v+8b\le250$$$$b\ge2v$$
   • $$12v+8b\ge250$$$$b\ge2v$$
   • $$12v+8b\le250$$$$v\ge2b$$
   • $$12v+8b\ge250$$$$v\ge2b$$

9. A number $$x$$ is at most $$5$$ less than $$4$$ times a number $$y$$. If $$y=3$$, what is the greatest possible value of $$x$$?

   • 7

10. A concert venue charges a flat fee of $$50$$ dollars plus $$15$$ dollars per person. If the budget is $$500$$ dollars, what is the maximum number of people that can attend?

    • 30