Setting Up Equations

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Algebra II › Setting Up Equations

Questions 1 - 10
1

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?

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

(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.

2

Set up the equation: Nine more than three times the cube of a number is four.

Explanation

Split the sentence into parts.

The cube of a number:

Three times the cube of a number:

Nine more than three times the cube of a number:

Is four:

Combine the parts to form the equation.

The answer is:

3

Set up the equation: Eight less than four times a number is twenty.

Explanation

Split the sentence into parts.

Four times a number:

Eight less than four times a number:

Is twenty:

Set the terms equal.

The answer is:

4

Two numbers have a ratio of 5:6 and half of their sum is 22. What are the numbers?

Explanation

Set up the equation:

Solve the equation:

Find the two numbers:

The two numbers have a ratio of 5:6, therefore the ratio can also be represented as:

The two numbers are 20 and 24.

5

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 . 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.

6

Express as an equation.

more than is

Explanation

Take every word and translate into math.

more than means that you need to add to something which is .

Anytime you see "is" means equal.

Now let's combine and create an expression of

7

Set up the following equation: The sum of a number and twice the square of a number is eleven.

Explanation

Break up the sentence into parts.

Twice the square of a number:

The sum of a number and twice the square of a number:

Is eleven:

Combine the parts to form the equation.

The answer is:

8

Set up the equation: Five less than three times a number is eight.

Explanation

Break up the sentence into parts.

Three times a number:

Five less than three times a number:

Is eight:

Combine the parts to form the equation.

The answer is:

9

Write in slope-intercept form

Explanation

Recall the form for slope-intercept as follows.

where represents the slope and is the y-intercept.

Given the equation in this question, first distribute the one fourth to both terms inside the parentheses.

Next, subtract two from both sides to isolate y.

This results in the slope-intercept form of the equation.

10

Set up the equation: Half of the cube root of twice a number is seven.

Explanation

Break up the sentence into parts.

Twice a number:

Cube root of twice a number:

Half the cube root of twice a number:

Is seven:

Combine the parts to form the equation.

The answer is:

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