Algebra 1 : How to write expressions and equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #937 : Algebra 1

In a room full of 60 people, 32 are women and 20 have blonde hair. Of the men, 16 do not have blonde hair. How many blonde women are in the room?

Possible Answers:

Correct answer:

Explanation:

First, calculate the total number of men.

Next, calculate the number of blonde men.

Now we can calculate the number of blonde women.

Example Question #21 : How To Write Expressions And Equations

A train travels for 2.5 hours at 60mph. For the next hour, the train travels at 40mph. How far does the train travel over the course of 3.5 hours?

Possible Answers:

Correct answer:

Explanation:

Use the distance equation, where is distance (mi),  is rate (mph), and  is time (h). In this instance, the train is traveling in two segments, so we will add the distances traveled during each segment.

The first rate is 60mph, and the first time is 2.5 hours. The second rate is 40mph, and the second time is 1 hour.

Example Question #939 : Algebra 1

The sum of two numbers is forty, and one number is three less than twice the other number.

Write an equation that represents this sentence.

Possible Answers:

Correct answer:

Explanation:

Suppose one number is .

The other number is "three less than twice the other number." Twice our other number is , and three less than twice this number is .

We are told that the sum of these two numbers is forty.

Now we can simplify.

Example Question #940 : Algebra 1

Represent this number in scientific notation:

Possible Answers:

Correct answer:

Explanation:

Write this number with the decimal point after it.

Move the decimal point to the position after the first nonzero digit, which here is the 1. Note that the resulting number, after truncating the trailing zeroes, is 

.

Also note that the number of places the decimal point moved is 23. Since the point was moved left the exponent will be 23, and the correct choice is 

.

Example Question #22 : How To Write Expressions And Equations

A barrel of oil is full. After adding 240 liters of oil to the barrel, it is full. What is the capacity of the oil barrel?

Possible Answers:

Correct answer:

Explanation:

When 240 liters of oil were added to the barrel, the barrel's volume increased by . Therefore, of the barrel's capacity must equal 240 liters. If is the barrel's capacity, then . Solving for this equation gives you a solution of 640, which is the barrel's capacity.

Example Question #23 : How To Write Expressions And Equations

We have two integers that add up to 66. If one integer is five times the other one, what is the value of this other integer?

Possible Answers:

none of these

Correct answer:

Explanation:

First, we have to translate the question into an equation. So we have two integers. Let's call one of the integers .  The second integer is 5 times greater than the other one. Thus, we call this .  Both  and  are suppose to add up to 66. So mathematically, this is written as

We just solve for .

So the value of the integer is 11.

Example Question #24 : How To Write Expressions And Equations

Two integers add up to 84. One of the integers is 2 units less than the other one. Find this other integer.

Possible Answers:

Correct answer:

Explanation:

We will call this other integer .  Since the first integer is 2 units less than this other one, it is written as .  Both  and  add up to 84.  This is mathematically written as

Solve for .

 

Example Question #25 : How To Write Expressions And Equations

A glass jar full of nickels and dimes is worth $19.80. If the jar has 15 more nickels than dimes, how many nickels and dimes are in the jar?

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

The expression representing nickels and dimes making up $19.80 is

Where  is the number of nickels and  is the number of dimes. Notice that the number of nickels and dimes are multiplied by their values (i.e.  is multiplied by 0.05 because each nickel is worth 5 cents).  It is given that there are 15 more nickels than there are dimes.  This is represented as

and thus,

We can find the number of dimes by solving for .

So there are 127 dimes in the jar. Use this to find the number of nickels

So there are 142 nickels and 127 dimes in the jar.

Example Question #26 : How To Write Expressions And Equations

Find the domain in interval notation of the following function:

Possible Answers:

Correct answer:

Explanation:

The function is not defined when  and

It is defined between

and

Example Question #27 : How To Write Expressions And Equations

Janet earned $800 babysitting this year. She plans to save ten percent of her income, but only after subtracting the amount she spent on gas money. Gas costs about $0.50/mile driven. Write an equation expressing the amount of money  from which Janet will calculate her savings after subtracting the amount spent on gas for the miles driven .

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

1) First step in writing an equation is always to define variables:

total earnings left after subtracting gas money

miles driven

2) Look at the given information. We know Janet starts with $800. So that must be included in an equation detailing how to get from her initial income to her final earnings, and it cannot be dependent on anything, since she already has it:

3) We know she has to subtract gas money, and that the rate is $0.50 per mile, so:

4) It says that Janet must save ten percent. But the equation is only required to express the amount of money she earns prior to saving, so the ten percent is irrelevant to the equation.

 

So the final answer is

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