Section 2.2 Part 2: Translating Phrases to Algebraic Expressions (Writing Problems)

Translate the word phrase into an algebraic expression: 16x more than 7.

16x+7

A rabbit eats turnips and radishes. The number of turnips is four more than twice the number of radishes. Let n represent the number of radishes. Write the expression that gives the number of turnips.

2n+4 Write the phrase about the number of turnips the rabbit eats.four more than twice the number of radishesSubstitute n for the number of radishes.4 more than twice nTranslate "twice n" into algebra. 4 more than 2nTranslate "4 more than 2n" into algebra. 2n+4

The length of a rectangle is 6 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.

Solution: Write a phrase about the length of the rectangle. 6 less than the width,Substitute w for "the width." 6 less than w Rewrite "less than" as "subtracted from." 6 subtracted from w Translate the phrase into algebra. w−6

Question: June has dimes and quarters in her purse. The number of dimes is three less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.

Solution: Write the phrase about the number of dimes. three less than four times the number of quarters Substitute q for the number of quarters. 3 less than 4 times q Rewrite "4 times q" as the product 4q. 3 less than 4q Translate the phrase into algebra. 4q−3

Translate the word phrase into an algebraic expression: 11u divided into 2u.

The key words divided into tell us to divide the numbers. So, the phrase 11u divided into 2u means 2u÷11u. This can also be written as 2u/11u.

The number of students in a school's math club is ten less than twice the number of students in the art club. Let a represent the number of students in the art club. Write an expression for the number of students in the math club.

Translate "10 less than 2a" into algebra. answer is 2a−10

Question Paul and Cheryl sold candy bars for a fundraiser. Paul sold six less than three times the number of candy bars that Cheryl sold. If c represents the number of candy bars Cheryl sold, write an expression for the number of candy bars Paul sold.

Write the phrase about the number of candy bars Paul sold. six less than three times the number of candy bars Cheryl sold Substitute c for the number of candy bars Cheryl sold. 6 less than 3 times c Translate "3 times c" into algebra. 6 less than 3cTranslate "6 less than 3c" into algebra. 3c−6

Michael and Jacqueline work at a computer store. Michael sold five less than twice the number of computers that Jacqueline sold. If j represents the number of computers Jacqueline sold, write an expression for the number of computers Michael sold. Note: An expression does not have an equal sign.

Write the phrase about the number of computers Michael sold.five less than twice the number of computers that Jacqueline soldSubstitute j for the number of computers that Jacqueline sold.5 less than twice jTranslate "twice j" into algebra.5 less than 2jTranslate " 5 less than 2j" into algebra. 2j−5

Sarah and Andrew sold coupon books for a fundraiser. Sarah sold one more than three times the number of coupon books that Andrew sold. If a represents the number of coupon books Andrew sold, write an expression for the number of coupon books that Sarah sold. Provide your answer below:

Write the phrase about the number of coupon books Sarah sold.one more than three times the number of coupon books that Andrew sold Substitute a for the number of coupon books Andrew sold. 1 more than 3 times a Translate "3 times a" into algebra. 1 more than 3a Translate "1 more than 3a" into algebra. 3a+1

Ruth has pennies and dimes in her pocket. The number of dimes is twelve less than twice the number of pennies. Let p represent the number of pennies. Write an expression for the number of dimes. Note: An expression will not include an equal sign.

Write the phrase about the number of dimes Ruth has.the number of dimes is twelve less than twice the number of penniesSubstitute p for the number of pennies Ruth has.12 less than twice pTranslate "twice p" into algebra.12 less than "2p"Translate "12 less than 2p" into algebra. 2p−12

Translate the word phrase into an algebraic expression: a times 11a.

a(11a)

Arianna and William go shrimping. Arianna caught nine less than five times the number of shrimp that William caught. If c represents the number of shrimp William caught, write the expression that gives the number of shrimp that Arianna caught.

5c−9

Translate the word phrase into an algebraic expression: 14m plus 2.

14m+2

Translate the word phrase into an algebraic expression: eight times the sum of 7x and seven.

There are two operation words: times tells us to multiply and sum tells us to add. Because we are multiplying 8 times the sum, we need parentheses around the sum of 7x and 7. So, the phrase eight times the sum of 7x and seven means 8(7x+7).

The width of a rectangle is 6 less than the length. Let L represent the length of the rectangle. Write an expression for the width of the rectangle.

L-6

Translate the word phrase into an algebraic expression: the sum of nine times 3c and eleven.

To take a sum, we look for the words of and and to see what is being added. Here we are taking the sum of 9 times 3c and 11. So, the phrase the sum of nine times 3c and eleven means 9(3c)+11.

Translate the word phrase into an algebraic expression: seventeen times the difference of 14p and 9q.

17(14p-9q) There are two operation words: times tells us to multiply and difference tells us to subtract. Because we are multiplying 17 times the difference, we need parentheses around the difference of 14p and 9q. So, the phrase seventeen times the difference of 14p and 9q means 17(14p−9q).

Translate the word phrase into an algebraic expression: seventeen times the difference of 4t and 4u.

17(4t-4u)

Translate the word phrase into an algebraic expression: y subtracted from 7y.

7y-y

Douglas and Jesse play video games together. Douglas won two more than five times the number of games that Jesse won. If c represents the number of games Jesse won, write an expression for the number of games Douglas won.

2+5(c) Write the phase about the number of games Jesse won.Two more than five times the number of games.Substitute c for the number of games. 2 more than 5 times c.Translate "5 times c" into algebra. 2 more than 5cTranslate "2 more than 5c" into algebra. 5c+2

The number of students in a school's Spanish club is six less than twice the number of students in the art club. Let a represent the number of students in the art club. Write an expression for the number of students in the Spanish club.

2a-6 Write the phrase about the number of students in Spanish club.six less than twice the number of students in art clubSubstitute a for the number of students in art club.6 less than twice aTranslate "twice a" into algebra.6 less than 2aTranslate "6 less than 2a" into algebra. 2a−6

Jacqueline and Maria set up bug barns to catch lady bugs. Jacqueline caught ten more than three times the number of lady bugs that Maria caught. If c represents the number of lady bugs Maria caught, write an expression for the number of lady bugs that Jacqueline caught.

3c+10 Write the phrase about the number of lady bugs caught.ten more than three times the number of lady bugsSubstitute c for the number of lady bugs Maria caught.10 more than 3 times cTranslate "3 times c" into algebra.10 more than 3cTranslate "10 more than 3c" into algebra.3c+10

Question Gary and Angela hike mountains. Gary hiked eight less than three times the number of mountains that Angela hiked. If c represents the number of mountains Angela hiked, write the expression for the number of mountains Gary hiked.

3c−8 Write the phrase about the number of mountains hiked.Eight less than three times the number of mountains.Substitute c for the number of mountains Angela hiked.8 less than 3 times c.Translate "3 times c" into algebra. 8 less than 3c.Translate "8 less than 3c" into algebra. 3c−8

Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

7n+3