Section 2.3 Part 2: Translating Phrases to Algebraic Equations and Solving (MORE PROBLEMS)

Translate the word phrase into an algebraic equation and solve: twenty-eight subtracted from a gives twenty-two.

A=50

Translate the word phrase into an algebraic equation and solve: subtract twenty-nine from d is eight.

D=37

Translate the word phrase into an algebraic equation and solve: the difference of y and eleven gives two.

The key word difference tells us to subtract the two numbers. The numbers stay in the same order as in the phrase. So, the phrase the difference of y and eleven means y−11.The key word gives means "equals" so the entire phrase, the difference of y and eleven gives two, translates to the equation y−11=2. To solve an equation, we must isolate the variable. To isolate y we will add 11 to both sides and simplify. y−11=2 Y-11+11=2+11 Y=13

Translate the word phrase into an algebraic equation and solve: y plus seven is equal to seventeen.

Y=10

Translate the word phrase into an algebraic equation: five times the sum of 8u and eight gives one hundred sixty.

(8u + 8)5 = 160 There are two operation words: times tells us to multiply and sum tells us to add. Because we are multiplying 5 by the sum, we need parentheses around the sum of 8u and 8. So, the phrase five times the sum of 8u and eight means 5(8u+8).The key word gives means "equals" so the entire phrase, five times the sum of 8u and eight gives 160, translates to the equation 5(8u+8)=160.

Translate the word phrase into an algebraic equation: one times the difference of 6p and one is seventeen.

1(6p−1)=17. There are two operation words: times tells us to multiply and difference tells us to subtract. Because we are multiplying 1 by the difference, we need parentheses around the difference of 6p and 1. So, the phrase one times the difference of 6p and one means 1(6p−1).The key word is means "equals" so the entire phrase, one times the difference of 6p and one is 17, translates to the equation 1(6p−1)=17.

Translate the word phrase into an algebraic equation: the difference of fourteen times 7m and seven is ninety-one.

14(7m)−7=91 To take a difference, we look for the words of and and to see what is being subtracted. Here we are taking the difference of 14 times 7m and 7. So, the phrase the difference of fourteen times 7m and seven means 14(7m)−7.The key word is means "equals" so the entire phrase, the difference of fourteen times 7m and seven is 91, translates to the equation 14(7m)−7=91.

Translate the word phrase into an algebraic equation: seventeen times the difference of 15x and twelve is five hundred sixty-one.

17(15X-12)=561 There are two operation words: times tells us to multiply and difference tells us to subtract. Because we are multiplying 17 by the difference, we need parentheses around the difference of 15x and 12. So, the phrase seventeen times the difference of 15x and twelve means 17(15x−12).The key word is means "equals" so the entire phrase, seventeen times the difference of 15x and twelve is 561, translates to the equation 17(15x−12)=561.