Basic Arithmetic : Creating Linear Equations with Part, Percent, and Whole

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

Example Question #1 : Creating Linear Equations With Part, Percent, And Whole

What is the perimeter of a semicircle with an area of ?

Possible Answers:

Correct answer:

Explanation:

This is a multi-step problem.  The perimeter of a semicircle is the sum of the circumference and diameter.  First, since we are given the area, we will need to find the radius.

For the area of a semicircle:

Since the area is , substitute this into A to find radius r.

Since the radius is 2, the diameter is 4.  

The circumference for a semicircle is:

The perimeter is the sum of the circumference and diameter:

 

Example Question #11 : Percents And Decimals

What is  of ?

Possible Answers:

Correct answer:

Explanation:

Before multiplying, it's necessary to convert 0.25% to a decimal, which is 0.0025.

Multiply this 0.0025, with 100.  

The correct answer is 0.25.

Example Question #12 : Percents And Decimals

What is  of ?

Possible Answers:

Correct answer:

Explanation:

Before multiplying, we can convert % into a decimal:  .

Answering our initial question:

Example Question #13 : Percents And Decimals

What is the perimeter of a rectangle with an area of , a length of , and a width of ?

Possible Answers:

Correct answer:

Explanation:

Based on the information given in the question, we know that . Since we also know the values of length  and width , however, we don't need to use the area equation to solve for  and , since the perimeter .

Substituting in the known values of  and :

Example Question #14 : Percents And Decimals

What is  of ?

Possible Answers:

Correct answer:

Explanation:

Before we answer the question, we should convert  into a decimal:  = .

We can then substitute this value into the original question:

Example Question #15 : Percents And Decimals

Lucy is a real estate agent who is paid a  commission on the value of each house she sells every month. She is also paid a base monthly rate of  as part of her salary. If  represents the value of the houses she sells per month, which of the following equations would accurately predict how much money she makes per month?

Possible Answers:

Correct answer:

Explanation:

To start, we need to convert the percent into a decimal.

Now, we know that Lucy receives 17% of the value of the homes she sells as her commission. Her commission can then be written as the expression .

Lucy is also paid $1000 regardless of if she sells any houses or not that month. In a linear equation, this would be our y-intercept.

Putting the pieces of the salary together, we get the following equation:

Example Question #16 : Percents And Decimals

A school board plans to renovate one of its schools in order to make room for more people. After the renovation, the school's maximum capacity will increase by 20%. If the school's current maximum capacity is 1020 people, what will its maximum capacity be after the renovation?

Possible Answers:

Correct answer:

Explanation:

A 20% increase is equal to 120% of the original value. To figure out how much more space the building will have if expanded 20%, you must multiply the existing maximum capacity (1020) by 120%. To do this, first divide 120 by 100.

Then, multiply the result times the existing maximum capacity.

The result is your answer.

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