Common Core: 7th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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Example Questions

Example Question #2 : How To Solve Two Step Equations

Write as an equation:

Twice the sum of a number and ten is equal to the difference of the number and one half.

Possible Answers:

Correct answer:

Explanation:

Let  represent the unknown number.

"The sum of a number and ten" is the expression . "Twice" this sum is two times this expression, or

.

"The difference of the number and one half" is a subtraction of the two, or

Set these equal, and the desired equation is

Example Question #1 : Solving Systems Of Equations In Word Problems

Mark is three times as old as his son Brian. In ten years, Mark will be  years old. In how many years will Mark be twice as old as Brian? 

Possible Answers:

Correct answer:

Explanation:

In ten years, Mark will be  years old, so Mark is  years old now, and Brian is one-third of this, or  years old. 

Let  be the number of years in which Mark will be twice Brian's age. Then Brian will be , and Mark will be . Since Mark will be twice Brian's age, we can set up and solve the equation:

Mark will be twice Brian's age in  years.

Example Question #1 : Word Problems

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is  years old?

Possible Answers:

Not enough information is given to determine the answer.

Correct answer:

Explanation:

Since Gary will be 37 in five years, he is  years old now. He is twice as old as Cathy, so she is  years old, and in five years, she will be  years old.

Example Question #1 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of  and has a perimeter of , then what is the length? 

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the  to one side of the equation. In order to do this, we will first subtract  from both sides of the equation. 

Next, we can divide each side by 

The length of the rectangle is 

Example Question #1 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of  and has a perimeter of , then what is the length? 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the  to one side of the equation. In order to do this, we will first subtract  from both sides of the equation. 

Next, we can divide each side by 

The length of the rectangle is 

Example Question #1 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of  and has a perimeter of , then what is the length? 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the  to one side of the equation. In order to do this, we will first subtract  from both sides of the equation. 

Next, we can divide each side by 

The length of the rectangle is 

Example Question #2 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of  and has a perimeter of , then what is the length? 

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the  to one side of the equation. In order to do this, we will first subtract  from both sides of the equation. 

Next, we can divide each side by 

The length of the rectangle is 

Example Question #3 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of  and has a perimeter of , then what is the length? 

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the  to one side of the equation. In order to do this, we will first subtract  from both sides of the equation. 

Next, we can divide each side by 

The length of the rectangle is 

Example Question #1 : Solving Linear Equations In Word Problems

If a rectangle possesses a width of  and has a perimeter of , then what is the length? 

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the  to one side of the equation. In order to do this, we will first subtract  from both sides of the equation. 

Next, we can divide each side by 

The length of the rectangle is 

Example Question #11 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

If a rectangle possesses a width of  and has a perimeter of , then what is the length? 

 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the  to one side of the equation. In order to do this, we will first subtract  from both sides of the equation. 

Next, we can divide each side by 

The length of the rectangle is 

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