Equations

Help Questions

Algebra 2 › Equations

Questions 1 - 10

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

$\frac{11}{3}$

$\frac{2}{3}$

$\frac{1}{18}$

$\frac{1}{5}$

Explanation

Add four on both sides.

$\frac{3x}{2}-4+4=5+4$

$\frac{3x}{2} = 9$

To isolate the x-variable, we will need to multiply by two thirds on both sides.

$\frac{3x}{2} \cdot \frac{2}{3} = 9 \cdot \frac{2}{3}$

The answer is:

A large tub has two faucets. The hot water faucet, if turned all the way up, can fill the tub in 16 minutes; the cold water faucet, in 12 minutes. Which of the following choices comes closest to the amount of time it takes for both faucets working together to fill the tub?

$7 \textup{ min}$

$8 \textup{ min}$

$5 \textup{ min}$

$6 \textup{ min}$

$4\textup{ min}$

Explanation

Work problems can be solved by looking at them as rate problems.

The hot faucet can fill up the tub at a rate of 16 minutes per tub, or $\frac{1}{16}$ tub per minute. The cold faucet, similarly, can fill up the tub at a rate of 12 minutes per tub, or $\frac{1}{12}$ tub per minute.

Suppose the tub fills up in minutes. Then, at the end of this time, the hot faucet has filled up $\frac{1}{16} X$ tub, and the cold faucet has filled up $\frac{1}{12} X$ tub, for a total of one tub. We can set up this equation and solve for :

$\frac{1}{16} X + \frac{1}{12} X = 1$

$48 \cdot \left (\frac{1}{16} X + \frac{1}{12} X \right )= 48 \cdot 1$

$48 \cdot \frac{1}{16} X + 48 \cdot \frac{1}{12} X = 48$

$7X\div 7 = 48 \div 7$

$X \approx 6.86$

Of the given choices, 7 minutes comes closest.

Solve the equation:

$\frac{2}{5}$

$\frac{2}{13}$

$-\frac{2}{13}$

$\frac{20}{13}$

Explanation

Add on both sides.

Combine like-terms on both sides.

Subtract nine from both sides.

Divide by five on both sides.

$\frac{5x}{5}=\frac{2}{5}$

The answer is: $\frac{2}{5}$

Tom is painting a fence feet long. He starts at the West end of the fence and paints at a rate of feet per hour. After hours, Huck joins Tom and begins painting from the East end of the fence at a rate of feet per hour. After hours of the two boys painting at the same time, Tom leaves Huck to finish the job by himself.

If Huck completes painting the entire fence after Tom leaves, how many more hours will Huck work than Tom?

$6\ hours$

$10\ hours$

$4\ hours$

$3\ hours$

$5\ hours$

Explanation

Tom paints for a total of hours (2 on his own, 2 with Huck's help). Since he paints at a rate of feet per hour, use the formula

$distance = rate \times time$ (or )

to determine the total length of the fence Tom paints.

feet

Subtracting this from the total length of the fence feet gives the length of the fence Tom will NOT paint: feet. If Huck finishes the job, he will paint that feet of the fence. Using , we can determine how long this will take Huck to do:

hours.

If Huck works hours and Tom works hours, he works more hours than Tom.

A circular tower stands surrounded by a circular moat. A bridge provides a passage over the moat to the tower. The distance from the outer edge of the moat to the center of the tower is meters. The area of the floor of tower is $4900\pi$ $m^{2}$ . How long is the bridge over the moat?

Explanation

The distance from the outer edge of the moat to the center of the castle is the radius (100 m) of the larger circle formed by the outer edge of the circular moat.

The radius of the tower's floor (found using the area of the floor), needs to be subracted from 100 m to find the distance fo the bridge.

$\sqrt{4900}=70$