Equations — Quiz 4

Questions in this quiz (8)

1. Let $$p$$ and $$q$$ be positive integers such that one-fourth of $$p$$ is $$q$$ less than one-third of $$p$$. Which of the following is a possible value of $$p$$?

   • $$18$$
   • $$24$$
   • $$30$$
   • $$38$$

2. Solve for $$m$$ in the equation: $$\sqrt{98}+\sqrt{98}=m\sqrt{n}$$ where $$m$$ and $$n$$ are integers such that $$m$$ > $$n$$. Which of the following is the value of $$m$$?

   • $$12$$
   • $$2$$
   • $$14$$
   • $$98$$

3. A new drink mixture is made of juice concentrate and water. There are $$12$$ ml of juice concentrate, and the total volume of the drink is $$20$$ ml. If the drink mixture is $$85\%$$ juice concentrate, what is the equation to solve for the amount of water, $$W$$, in the solution?

   • $$12(0.15)+W(0.85)=20$$
   • $$12(0.85)+W(1+W)=20$$
   • $$10.2+W(0.85)=20$$
   • $$12+W=20$$

4. A library charges a late fee of $$20$$ dollars for the first overdue book and $$10$$ dollars for each additional overdue book. Which of the following equations represents the total amount in fees, $$d$$ dollars, a borrower must pay for $$n$$ overdue books?

   • $$d=20+10n$$
   • $$d=20-10n$$
   • $$d=10+20n$$
   • $$d=10n+10$$

5. A drone is descending at a constant speed towards the ground. The table below shows the altitude, $$h$$ meters, of the drone at 1-second intervals from $$t=0$$ seconds to $$t=5$$ seconds.Which of the following equations represents this data?

   • $$h = 10t + 15$$
   • $$h = -10t - 150$$
   • $$h = 10t + 150$$
   • $$h = -10t + 150$$

6. If $$\frac{2}{x} + \frac{1}{4x} = 5$$, what is the value of $$x$$?

   • $$\frac{9}{5}$$
   • $$\frac{2}{9}$$
   • $$\frac{5}{9}$$
   • $$\frac{9}{20}$$

7. Solve the equation:$$\frac{6x-1}{3x+2}=\frac{6x+1}{3x-2}$$

   • 0
   • 1
   • -1
   • Infinite solutions

8. Solve the equation:$$\frac{\frac{5x}{4} - \frac{8}{9}}{\frac{7}{8}} = \frac{2}{3}x$$

   • $$\frac{7}{8}$$
   • $$\frac{45}{32}$$
   • $$\frac{4}{3}$$
   • $$\frac{1}{4}$$