Heart of Algebra: Linear Equations — Quiz 3

Questions in this quiz (10)

1. A farmer begins with $$18{,}000$$ pounds of grain. After $$4$$ hours, $$14{,}800$$ pounds remain. If the grain is removed at a constant rate, how many total hours will the farmer have been removing grain when $$10{,}400$$ pounds remain?

   • $$6.5$$
   • $$8$$
   • $$9.5$$
   • $$12$$

2. Emily paid a total of $$210$$ dollars for a bicycle by making a down payment of $$30$$ dollars plus monthly payments of $$15$$ dollars each. Which equation represents this situation?

   • $$15p-30=210$$
   • $$15p+30=210$$
   • $$30p+15=210$$
   • $$30p-15=210$$

3. A teacher is setting up $$6$$ stations. Each station will use either Kit A or Kit B, but not both. Kit A requires $$5$$ markers, and Kit B requires $$3$$ markers. If $$x$$ stations use Kit A and the rest use Kit B, which expression represents the total number of markers needed?

   • $$5x$$
   • $$3x+18$$
   • $$5x+3(6-x)$$
   • $$8x+18$$

4. Liam earns $$p$$ dollars per hour for the first $$8$$ hours of work and $$1.5$$ times that rate for each additional hour. One day, Liam worked $$9$$ hours and earned $$117$$ dollars. What is Liam's regular hourly wage?

   • $$10.7$$
   • $$11.5$$
   • $$12.3$$
   • $$13.4$$

5. In the equation $$3x+9=\frac{a(x+3)}{3}$$ $$a$$ is a constant. If the equation has infinitely many solutions, what is the value of $$a$$?

   • $$3$$
   • $$6$$
   • $$9$$
   • $$12$$

6. A factory produces $$8$$-inch, $$6$$-inch, and $$4$$-inch pipes. The number of $$8$$-inch pipes is $$3$$ times the number $$n$$ of $$6$$-inch pipes, and the number of $$4$$-inch pipes is $$12$$. The factory produces $$90$$ pipes total. Which equation represents this situation?

   • $$3n+n+12=90$$
   • $$8(3n)+6n+4(12)=90$$
   • $$3n+12=90$$
   • $$4n+12=90$$

7. A real estate company bought a property for $$80{,}000$$ dollars after receiving a $$20\%$$ discount and then an additional $$25\%$$ discount on the reduced price. Which of the following best approximates the original price of the property in dollars?

   • $$120{,}000.67$$
   • $$130{,}000.57$$
   • $$133{,}333.33$$
   • $$150{,}000.45$$

8. If $$52=20+4(x-6)$$, what is the value of $$4(x-6)$$?

   • $$16$$
   • $$24$$
   • $$32$$
   • $$36$$

9. A product costs a company $$50$$ to make. It is sold for $$80$$, and a salesperson earns a commission equal to $$10\%$$ of the sales price. The profit per unit is the sales price minus the cost and the commission. Which equation represents selling $$u$$ units to make a total profit of $$3{,}600$$?

   • $$(80-50-0.1(80))u=3{,}600$$
   • $$(80-50)(1-0.1)u=3{,}600$$
   • $$(0.1(80)+50)u=3{,}600$$
   • $$(80-0.1(80)-50u)=3{,}600$$

10. If $$\frac{1}{3}x-\frac{1}{9}x=2$$, what is the value of $$x$$?

    • $$3$$
    • $$6$$
    • $$9$$
    • $$12$$