Name: _____________________________ NOTES:

Translating and Solving Word Problems

Introduction of the “LET” statement. Set-up of word problem, equation and solution

Example: Eight times a number equals thirty-five more than the number. Find the number.

(set up) Let x = the number

(equation) 8 x=35+x

(solve!)

1. If three times a number is increased by twenty-two, the result is fourteen less than seven times the number. Find the number.

2. The second of three numbers is one less than the first. The third number is five less than the second. If the first number is twice as large as the third, find the three numbers.

[hint: your set-up is going to have three parts to it!!!]

Name: _________________________________ HOMEWORK:

Identify each part of the verbal expressions and then write an algebraic expression from each verbal expression.

1. 3 times a number ______________________________1

2. 3 more than a number ______________________________

3. 3 decreased by a number ______________________________

4. 3 less than a number ______________________________

5. One third of a number ______________________________

6. 8 more than 3 times a number ______________________________

7. 7 less than 4 times a number ______________________________

8. 7 decreased by 4 times a number ______________________________

9. 9 less than twice a number ______________________________

10. 9 less than half a number ______________________________

11. 7 times a number, increased by 4 ______________________________

12. 7 times a number, increased by 4 times the number __________________________

Name: _________________________________ CLASSWORK

Write an equation and solve.

1. Sixty more than 9 times a number is 375. Find the number.

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2. The width of a rectangle is 32 which is 4 less than half the length. Find the length.

3. Three times the sum of a number and four is equal to 30. Find the number.

Name: _________________________________ CLASSWORK continued

4. Three minus the product of five and y is the same as −12. Find y .

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5. The quotient of m and 5 increased by 8 is 1. Find the number.

BONUS: If 4 is added to a certain number, the result divided by 2, that result multiplied by 5, and then 6 subtracted from that result, the answer is 29 . Can you find that number?

Name: _____________________________ NOTES: More Word Problems

What is a consecutive integer? ____________________________________________

n ,n+1 , n+2 , n+3 , n+4

Consecutive Even? __________________ Consecutive Odd? __________________

n ,n+2 , n+4 , n+6 , n+8

1. The sum of three consecutive numbers is 204. Find the numbers.

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2. Find three consecutive odd integers such that the sum of the first and third equals the sum of the second and 43.

3. Sara’s telephone service costs $21 per month plus $0.25 for each local call, and long-distance calls are extra. Last month, Sara’s bill was $36.64, and it included $6.14 in long-distance charges. How many local calls did she make?

Name: _____________________________ HOMEWORK: More Word Problems

Show all necessary steps to solve the following:

1. Find three consecutive integers with sum −99.

2. Find three consecutive integers with sum 168. Which is the greatest of the three?

3. Find three consecutive odd integers such that the sum of the first and third equals the sum of the second and 31.

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4. Robin spent $17 at an amusement park for admission and rides. If she paid $5 for admission and rides cost $3 each, what is the total number of rides that she went on?

Name: __________________________

5. If one-half of a number is 8 less than two-thirds of the number, what is the number?

6. Mario paid $44.25 in taxi fare from the hotel to the airport. The cab charged $2.25 for the first mile plus $3.50 for each additional mile. How many miles was it from the hotel to the airport?

HOMEWORK: More Word Problems continued

7. Every month, Omar buys pizzas to serve at a party for his friends. In May, he bought three more than twice the number of pizzas he bought in April. If Omar bought 15 pizzas in May, how many pizzas did he buy in April?

8. The sum of three consecutive odd integers is 18 less than five times the middle number. Find the three

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integers. [Only an algebraic solution can receive full credit.] 9. The sum of the ages of the three

Romano brothers is 63. If their ages can be represented as consecutive integers, what is the age of the middle brother?

Name: ______________________________ CLASSWORK

Write an equation and solve:

1. Three times the sum of a number and four is equal to five times the number, decreased by two. Find the number.

2. −5 decreased by half of a number is the same as 4 increased by one fourth of a number. Find the number.

3. One increased by 2 times the sum of a number and 4 is 29. Find the number.

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4. Five times a number n is three less than twice n. Find n .

Name: ______________________________ CLASSWORK continued

5. The product of 9 and a number increased by 4 is the same as 14 less than 3 times the number. Find the number.

BONUS: The second angle of a triangle is three times the first, and the third angle is six more than twice the first. Find the measure of each angle if the angles add up to 180 °.

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Name: _____________________________ CLASSWORK Work Space Next Page

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Name: ____________________________________________

(E)

(A)

(B)

(O)

(E)

(A)

(K)

(H)

(O)

(T)

(K)

(R)

Name: _____________________________ Translating and Solving Inequalities

Define a variable, write an inequality, and solve.

_____ 1. An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of each DVD player (d ) and a $30 profit on the sale of each cordless telephone (c ). The store wants to make a profit of at least $255.00 from

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its sales of DVD players and cordless phones. Which inequality describes this situation?

(1)75d+30c<255(2)75d+30c≤255(3)75d+30c>255(4)75d+30c≥255

_____ 2. Students in a ninth grade class measured their heights, h, in centimeters. The height of the shortest student was 155 cm, and the height of the tallest student was 190 cm. Which inequality represents the range of heights?

(1)155<h<190(2)155≤h≤190(3)h≥155∨h≤190(4)h>155∨h<190

3. The sum of one third a number and 4 is at most the sum of twice that number and 12.

Name: ___________________________ Translating and Solving Inequalities continued

_____ 4. There are 461 students and 20 teachers taking buses on a trip to a museum. Each bus can seat a maximum of 52. What is the least number of buses needed for the trip? (1) 8 (2) 9 (3) 10 (4) 11

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5. You are taking a taxi in New York City. The driver charges an initial fare of $2.00 plus $1.75 for every mile driven. How far can you travel if you want to leave the driver a $3.50 tip, and you want to spend no more than $16.00?

6. Doug is selling brownies to raise money for a school club. He spent $8.50 to buy pans. The ingredients for each brownie cost $0.16. If he sells each brownie for $0.50, how many brownies does he need to sell before he starts making a profit?

Name: ___________________________ Translating and Solving Inequalities continued

7. One third of the sum of 5 times a number and 3 is less than one fourth the sum of six times that number and five.

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8. Ray had scores of 75 ,82 ,94 ,∧77 on his first four science tests. What must he score on the next test to have an average of at least 85?

9. Chelsea has $45 to spend at the fair. She spends $20 on admission and $15 on snacks. She wants to play a game that cost $0.65 per game. Write an inequality to find the maximum number of times, x, Chelsea can play the game. Using this inequality, determine the maximum number of times she can play the game.

Name: _____________________________ UNIT #2 = Review Part I

1. The product of −4 and an unknown number is −52. Which equation matches this situation?

(1) −4 x=−52

(2) −52 x=−4

(3) x−52

=−4

(4) −4x =−52

2. Which equation could be used to solve: 3 less than 5 times a number is 22.

(1) 225 n=3

(2) 5n−3=22

(3) 3−5n=22

(4) 5n=3−11

3. Eight less than four times a number n is 48. Choose the appropriate equation.

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(1) 8−4 n=48

(2) 8<4n+48

(3) 4 n−8=48

(4) 48−4=8n

4. Use an equation to model the sentence. How many raisins are left in the jar of 37 raisins after you have eaten some?

(1) R=37+N

(2) R= N37

(3) R=37N

(4) R=37−N

5. Mr. and Mrs. Sogard borrowed $4,200 from a bank, so that they could purchase an automobile. The interest on the loan was $25 per month. They paid the loan back in three years with equal monthly payments. Choose the equation that can be used to calculate p the Sogard’s monthly payment.

(1) p= 4 ,20036+25

(2) p=[ (4,200 ) (3 ) (12 )]÷36

(3) p= (4 ,200÷3 )+25

(4) p= (4,200 ) (3 ) (12 )+25

Name: __________________________

6. Use an equation to model the number of bagels remaining in a package from which 4 bagels have been eaten.

7. You are 3 times older than your younger sister and you are 12 years old. Write an equation to solve for your sister’s age. Will you be 3 times her age next year?

8. The sum of Scott’s age and Greg’s age is 33 years. If Greg’s age is represented by g. Scott’s age is represented by:

(1) 33−g

(2) g−33

(3) g+33

(4) 33 g

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UNIT #2 = Review Part I continued

9. In the Ambrose family, the ages of the three children are three consecutive even integers. If the age of the youngest child is represented by x+3, which expression represents the age of the oldest child?

(1) x+5

(2) x+6

(3) x+7

(4) x+8

10. Which expression represents the number of yards in x feet?

(1) x12

(2) x3

(3) 3 x

(4) 12 x

11. Tara buys two items that cost d dollars each. She gives the cashier $20. Which expression represents the change she should receive?

(1) 20−2d

(2) 20−d

(3) 20+2d

(4) 2d−2

Name: _____________________________ Unit 2 REVIEW Part II

1. John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation could be used to determine the number of dimes, x, in his pocket?

(1) 0.10 ( x+4 )+0.05(x )=$ 1.25

(2) 0.05 ( x+4 )+0.10 ( x )=$1.25

(3) 0.10 (4 x )+0.05 ( x )=$1.25

(4) 0.05 (4 x )+0.10 ( x )=$1.25

2. A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is $0.05 per megabyte. If d represents the number of additional megabytes used and c represents the total charges at the end of the month, which linear equation can be used to determine a user’s monthly bill?

(1) c=60−0.05d

(2) c=60.05d

(3) c=60d−0. 0516

(4) c=60+0.05d

3. Caitlin has a movie rental card worth $175. After she rents the first movie, the card’s value is $172.25. After she rents the second movie, its value is $169.50. After she rents the third movie, the card is worth $166.75 .

a) Assuming the pattern continues, write an equation to define A (n ), the amount of money on the rental card after n rentals.

b) Caitlin rents a movie every Friday night. How many weeks in a row can she afford to rent a movie, using her rental card only? Explain how you arrived at your answer.

Name: ____________________________________ Unit 2 REVIEW Part II continued

4. A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it with a width of x meters, as shown in the diagram below. Together, the walkway and the garden have an area of 396 square meters.

Write an equation that can be used to find x, the width of the walkway.

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Describe how your equation models the situation.

Determine and state the width of the walkway, in meters.

Name: ____________________________________ Unit 2 REVIEW Part II continued

5. An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for each dog. Pat noticed that the shelter spend $89.50 caring for cats and dogs on Wednesday.

Write an equation to represent the possible number of cats and dogs that could have been at the shelter on Wednesday.

Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s numbers possible? Use your equation to justify your answer.

Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on Wednesday. How many cats were at the shelter on Wednesday?

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