Heart of Algebra: Linear Inequalities — Quiz 3

Questions in this quiz (8)

1. A park can plant no more than $$200$$ trees. The number of oak trees is at most twice the number of pine trees. Which system represents this?

   • $$o+p\le200$$$$o\le2p$$
   • $$o+p\ge200$$$$o\le2p$$
   • $$o+p\le200$$$$o\ge2p$$
   • $$o+p\ge200$$$$o\ge2p$$

2. A shipping company requires that the perimeter of the base of a rectangular box plus the height cannot exceed $$100$$ inches. A box has height $$40$$ inches, and its length is $$2$$ times its width. Which inequality shows the allowable width $$x$$, in inches?

   • $$0$$ < $$x \le10$$
   • $$0$$ < $$x\le15$$
   • $$0$$ < $$x\le20$$
   • $$0$$ < $$x\le30$$

3. A student will spend at most $$96$$ dollars to buy $$x$$ notebooks and $$y$$ binders. The inequality $$9x+12y\le96$$ represents this situation. Which is the best interpretation of $$12y$$?

   • $$\text{The price of each binder}$$
   • $$\text{The price of each notebook}$$
   • $$\text{The total cost of the binders}$$
   • $$\text{The total cost of the notebooks}$$

4. In a survey of $$250$$ students, $$40$$ students chose soccer as their favorite sport. Among the remaining $$210$$ students, $$p$$ students chose soccer. If more than $$30\%$$ of all students chose soccer, which inequality describes the possible values of $$p$$?

   • $$p$$>$$0.30(250-40)$$$$p\le210$$
   • $$p$$>$$0.30(250+40)$$$$p\le210$$
   • $$p-40$$>$$0.30(250)$$$$p\le210$$
   • $$p+40$$>$$0.30(250)$$$$p\le210$$

5. The point $$(x,16)$$ is a solution to the system of inequalities $$y$$>$$10$$ and $$3x+y$$<$$25$$. Which of the following could be the value of $$x$$?

   • $$-4$$
   • $$3$$
   • $$5$$
   • $$8$$

6. A salesperson earns a base salary of $$x$$ dollars plus $$15\%$$ of total sales $$s$$. This year, the salesperson wants total earnings to be at least twice and at most $$3$$ times the base salary. Which inequality represents all possible values of $$s$$?

   • $$x\le s\le2x$$
   • $$\frac{x}{0.15}\le s\le\frac{2x}{0.15}$$
   • $$2x\le s\le3x$$
   • $$\frac{2x}{0.15}\le s\le\frac{3x}{0.15}$$

7. Which point $$(x,y)$$ is a solution to the inequality $$y$$ < $$-3x+6$$?

   • $$(-2,15)$$
   • $$(0,7)$$
   • $$(2,-1)$$
   • $$(3,0)$$

8. An electric circuit has a resistance of $$300$$ ohms. The potential difference is generated by $$n$$ batteries that each produce $$9$$ volts, for a total potential difference of $$9n$$ volts. If the current must be no more than $$0.18$$ ampere, what is the greatest number of batteries that can be used? $$I=\frac{V}{R}$$

   • 6