Solving Equations 2 — Heart of Algebra

Questions in this quiz (10)

1. If $$\frac{5}{m-3}=\frac{y}{4}$$ where $$m\ne3$$, what is $$m$$ in terms of $$y$$?

   • $$\frac{20-3y}{y}$$
   • $$\frac{20}{y}+3$$
   • $$\frac{20+3y}{y}$$
   • $$\frac{y}{20+3y}$$

2. Doctors use Young’s rule to determine the proper dosage $$d$$ in milligrams of a medication for a child based on the adult dosage $$a$$ in milligrams and the child’s age $$c$$ in years:$$d=a\left(\frac{c}{c+12}\right)$$A doctor prescribes a dosage for a child that is $$\frac{1}{3}$$ of the adult dosage. What is the child’s age in years?

   • $$6$$
   • $$12$$
   • $$16$$
   • $$24$$

3. A number increased by $$6$$ is equal to twice the number minus $$4$$. What is the number?

   • $$5$$
   • $$8$$
   • $$10$$
   • $$14$$

4. Solve for $$x$$:$$\frac{3}{2}(x-4)+5=\frac{1}{2}(3x+2)$$

   • $$3$$
   • $$4$$
   • $$5$$
   • No solution

5. The sum of three times a number and $$8$$ is equal to twice the number plus $$17$$. What is the number?

   • $$\frac{17}{2}$$
   • $$8$$
   • $$9$$
   • $$\frac{17}{8}$$

6. A tank is filled using two pipes. Pipe A fills the tank at a rate of $$\frac{1}{4}$$ tank per hour, and Pipe B fills the tank at a rate of $$\frac{1}{6}$$ tank per hour. If both pipes work together, how many hours will it take to fill the tank completely?

   • $$\frac{1}{12}$$
   • $$\frac{1}{2}$$
   • $$\frac{12}{5}$$
   • $$\frac{5}{12}$$

7. If $$(3x-4)(bx+5)=3bx^2+7x-20$$ for all values of $$x$$, what is the value of $$b$$?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$5$$

8. A movie theater charges a fixed admission fee plus a cost per ticket. Three tickets cost $$29$$ dollars, and five tickets cost $$41$$ dollars. What is the fixed admission fee, in dollars?

   • $$7$$
   • $$11$$
   • $$17$$
   • $$23$$

9. If $$\frac{4}{x-3}-\frac{2}{x+3}=0$$, what is the value of $$x$$?

   • $$-9$$
   • $$6$$
   • $$12$$
   • $$18$$

10. A pendulum’s period $$t$$, in seconds, is modeled by the formula:$$t=2\pi\sqrt{\frac{L}{g}}$$where $$L$$ is the length of the pendulum in meters and $$g$$ is the acceleration due to gravity in meters per second squared. If a pendulum has a length of $$4$$ meters and a period of $$4\pi$$ seconds, what is the value of $$g$$?

    • $$1$$
    • $$2$$
    • $$4$$
    • $$6$$