Common Core: 6th Grade Math : Use Variables to Represent Numbers and Write Expressions: CCSS.Math.Content.6.EE.B.6

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

Example Question #1 : How To Find The Solution To An Equation

James bought candy using a 10 dollar bill and received \displaystyle y dollars in change.  Which of the following describes how much James paid for the candy?

Possible Answers:

\displaystyle 10+y

\displaystyle y/10

\displaystyle 10-y

\displaystyle 10/y

\displaystyle y-10

Correct answer:

\displaystyle 10-y

Explanation:

The amount of change given after a purchase is the amount the customer pays minus the cost of the item.  So the cost of the item is the amount the customer pays minus the amount of change received.

Example Question #2 : How To Find The Measure Of An Angle

Call the three angles of a triangle \displaystyle \angle 1, \angle 2, \angle 3

The measure of \displaystyle \angle2 is twenty degrees greater than that of \displaystyle \angle 1; the measure of \displaystyle \angle 3 is thirty degrees less than twice that of \displaystyle \angle 1. If \displaystyle x is the measure of \displaystyle \angle 1, then which of the following equations would we need to solve in order to calculate the measures of the angles?

Possible Answers:

\displaystyle x + (x-20) + 2(x-30) = 180

\displaystyle x + (x+20) = (2x+30)

\displaystyle x + (x+20) + (2x-30) = 360

\displaystyle x + (x+20) + (2x-30) = 180

\displaystyle x + (x-20) + 2(x-30) = 360

Correct answer:

\displaystyle x + (x+20) + (2x-30) = 180

Explanation:

The measure of \displaystyle \angle2 is twenty degrees greater than the measure \displaystyle x of \displaystyle \angle 1, so its measure is 20 added to that of \displaystyle \angle 1 - that is, \displaystyle x + 2 0.

The measure of \displaystyle \angle 3 is thirty degrees less than twice that of \displaystyle \angle 1. Twice the measure of \displaystyle \angle 1 is \displaystyle 2x, and thirty degrees less than this is 30 subtracted from \displaystyle 2x - that is, \displaystyle 2x-30.

The sum of the measures of the three angles of a triangle is 180, so, to solve for \displaystyle x - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

\displaystyle x + (x+20) + (2x-30) = 180

Example Question #3 : How To Find The Measure Of An Angle

Call the three angles of a triangle \displaystyle \angle 1, \angle 2, \angle 3

The measure of \displaystyle \angle2 is forty degrees less than that of \displaystyle \angle 1; the measure of \displaystyle \angle 3 is ten degrees less than twice that of \displaystyle \angle 1. If \displaystyle x is the measure of \displaystyle \angle 1, then which of the following equations would we need to solve in order to calculate the measures of the angles?

Possible Answers:

\displaystyle x + (x-40) + 2 (x - 10) = 360

\displaystyle x + (x-40) + 2 (x - 10) = 180

\displaystyle x + (x-40) = (2x - 10)

\displaystyle x + (x-40) + (2x - 10) = 180

\displaystyle x + (x-40) + (2x - 10) = 360

Correct answer:

\displaystyle x + (x-40) + (2x - 10) = 180

Explanation:

The measure of \displaystyle \angle2 is forty degrees less than the measure \displaystyle x of \displaystyle \angle 1, so its measure is 40 subtracted from that of \displaystyle \angle 1 - that is, \displaystyle x -40.

The measure of \displaystyle \angle 3 is ten degrees less than twice that of \displaystyle \angle 1. Twice the measure of \displaystyle \angle 1 is \displaystyle 2x, and ten degrees less than this is 10 subtracted from \displaystyle 2x - that is, \displaystyle 2x-10.

The sum of the measures of the three angles of a triangle is 180, so, to solve for \displaystyle x - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

\displaystyle x + (x-40) + (2x - 10) = 180

Example Question #1 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Read the following scenario:

A barista has to make sixty pounds of a special blend of coffee at Moonbucks, using Hazelnut Happiness beans and Pecan Delight beans. If there are fourteen fewer pounds of Hazelnut Happiness beans in the mixture than Pecan Delight beans, then how many pounds of each will she use?

If \displaystyle x represents the number of pounds of Pecan Delight coffee beans in the mixture, then which of the following equations could be set up in order to find the number of pounds of each variety of bean?

Possible Answers:

\displaystyle x + (x - 14) = 60

\displaystyle x + (x - 60) = 14

\displaystyle x + (14-x) = 60

\displaystyle x + (x + 60) = 14

\displaystyle x + (x + 14) = 60

Correct answer:

\displaystyle x + (x - 14) = 60

Explanation:

Since there are fourteen fewer pounds of Hazelnut Happiness beans in the mixture than Pecan Delight beans , then the number of pounds of Hazelnut Happiness beans is fourteen subtracted from \displaystyle x:

\displaystyle x -14.

Add the number of pounds of Pecan Delight beans, \displaystyle x, to the number of pounds of Hazelnut Happiness beans, \displaystyle x -14, to get the number of pounds of the mixture, which is \displaystyle 60.

This translates to the following equation:

\displaystyle x + (x - 14) = 60

Example Question #2 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Read the following scenario:

A barista has to make forty pounds of a special blend of coffee at Moonbucks, using Vanilla Dream beans and Strawberry Heaven beans. If there are twelve more pounds of Vanilla Dream beans in the mixture than Strawberry Heaven beans, then how many pounds of each will she use?

If \displaystyle x represents the number of pounds of Strawberry Heaven coffee beans in the mixture, then which of the following equations could be set up in order to find the number of pounds of each variety of bean?

Possible Answers:

\displaystyle x - (x + 40) = 12

\displaystyle x - (x + 12) = 40

\displaystyle x + (x - 12) = 40

\displaystyle x + (x + 40) = 12

\displaystyle x + (x + 12) = 40

Correct answer:

\displaystyle x + (x + 12) = 40

Explanation:

Since there are twelve more pounds of Vanilla Dream beans in the mixture than Strawberry Heaven beans, then the number of pounds of Vanilla Dream beans is twelve added to \displaystyle x:

 \displaystyle x + 12.

Add the number of pounds of Strawberry Heaven beans, \displaystyle x, to the number of pounds of Vanilla Dream beans, \displaystyle x + 12, to get the number of pounds of the mixture, which is \displaystyle 40.

This translates to the following equation:

\displaystyle x + (x + 12) = 40

Example Question #441 : Expressions & Equations

Select the equation or inequality that matches the number sentence below.

\displaystyle 93 is greater than \displaystyle x minus \displaystyle 45

Possible Answers:

\displaystyle 93< x-45

\displaystyle 92< 45-x

\displaystyle 93=x-45

\displaystyle 93>x-45

\displaystyle 93>45-x

Correct answer:

\displaystyle 93>x-45

Explanation:

Our number sentence has the phrase "greater than" which means we have an inequality. 

"\displaystyle 93 is greater than" can be written as \displaystyle 93> because we replace the words "greater than" with the greater than symbol. 

Next, we have "\displaystyle x minus \displaystyle 45". This can be written as \displaystyle x-45 because minus means subtraction, so we replace the word "minus" with the subtraction symbol. 

When we put these pieces together we have \displaystyle 93>x-45

 

Example Question #441 : Expressions & Equations

Select the equation or inequality that matches the number sentence below.

\displaystyle 14 is greater than \displaystyle x minus \displaystyle 19

 

Possible Answers:

\displaystyle 14< 19-x

\displaystyle 14=x-19

\displaystyle 14>x-19

\displaystyle 14=19-x

\displaystyle 14< x-19

Correct answer:

\displaystyle 14>x-19

Explanation:

Our number sentence has the phrase "greater than" which means we have an inequality. 

"\displaystyle 14 is greater than" can be written as \displaystyle 14> because we replace the words "greater than" with the greater than symbol. 

Next, we have "\displaystyle x minus \displaystyle 19". This can be written as \displaystyle x-19 because minus means subtraction, so we replace the word "minus" with the subtraction symbol. 

When we put these pieces together we have \displaystyle 14>x-19

Example Question #443 : Expressions & Equations

Select the equation or inequality that matches the number sentence below.

\displaystyle 72 is greater than \displaystyle x minus \displaystyle 31

 

Possible Answers:

\displaystyle 72< x-31

\displaystyle 72=31-x

\displaystyle 72< 31-x

\displaystyle 72>x-31

\displaystyle 72>31-x

Correct answer:

\displaystyle 72>x-31

Explanation:

Our number sentence has the phrase "greater than" which means we have an inequality. 

"\displaystyle 72 is greater than" can be written as \displaystyle 72> because we replace the words "greater than" with the greater than symbol. 

Next, we have "\displaystyle x minus \displaystyle 31". This can be written as \displaystyle x-31 because minus means subtraction, so we replace the word "minus" with the subtraction symbol. 

When we put these pieces together we have \displaystyle 72>x-31

Example Question #1 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Select the equation or inequality that matches the number sentence below.

\displaystyle 13 is less than \displaystyle x minus \displaystyle 21

 

Possible Answers:

\displaystyle 13< x-21

\displaystyle 13>x-21

\displaystyle 13>21-x

\displaystyle 13< 21-x

\displaystyle 13=x-21

Correct answer:

\displaystyle 13< x-21

Explanation:

Our number sentence has the phrase "less than" which means we have an inequality. 

"\displaystyle 13 is less than" can be written as \displaystyle 13<  because we replace the words "less than" with the less than symbol. 

Next, we have "\displaystyle x minus \displaystyle 21". This can be written as \displaystyle x-21 because minus means subtraction, so we replace the word "minus" with the subtraction symbol. 

When we put these pieces together we have \displaystyle 13< x-21

Example Question #3 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Select the equation or inequality that matches the number sentence below.

\displaystyle 57 is less than \displaystyle x minus \displaystyle 19

 

Possible Answers:

\displaystyle 57=19-x

\displaystyle 57< x-19

\displaystyle 57>19-x

\displaystyle 57< 19-x

\displaystyle 57>x-19

Correct answer:

\displaystyle 57< x-19

Explanation:

Our number sentence has the phrase "less than" which means we have an inequality. 

"\displaystyle 57 is less than" can be written as \displaystyle 57<  because we replace the words "less than" with the less than symbol. 

Next, we have "\displaystyle x minus \displaystyle 19". This can be written as \displaystyle x-19 because minus means subtraction, so we replace the word "minus" with the subtraction symbol. 

When we put these pieces together we have \displaystyle 57< x-19

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