Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test

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Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test Simplify: 1. 4 • 5 3 • 3 20 9 Common Denominator + + 4 • 6 8 24 • 3 24 29 Add 29 = 5 Or 1 24 24 24 2. 8 12 ÷ 25 35 Note: To divide fractions, we invert and multiply. 2 7 8 35 14 • = 25 12 15 5 3 Note: When multiplying, reduce any numerator with any denominator. © 2007-09 by S-Squared, Inc. All Rights Reserved.

Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test Simplify: 3. 69.03 + 5.09 Note: Line up decimal points and add. 69.03 + 5.09 74.12 74.12 4. 0.47 • 0.9 Note: Having three digits behind the decimal point before you multiply means three digits should be behind the decimal point in the answer. .47 x .9 .423 .423

Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test 5. a) Translate the equation: Eight more than three times a number is 20. 3x + 8 = 20 b) Solve the equation. 3x + 8 = 20 − 8 − 8 Subtract 3x = 12 Divide 3 3 x = 4

Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test 6. a) Translate the inequality: Four times the difference of a number and three is less than 16. 4(x – 3) < 16 b) Solve the inequality. 4(x – 3) < 16 Distribute 4x – 12 < 16 + 12 + 12 Add 4x < 28 4 4 Divide x < 7

Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test 7. The sum of 2 consecutive integers is 51. a) Write a variable equation for the given information. Assign variables: Let, x = the 1st integer and x + 1 = the 2nd integer x + x + 1 = 51 Simplify 2x + 1 = 51 b) Find the integers. 2x + 1 = 51 The first integer is x Subtract − 1 − 1 1st integer: 25 2x = 50 Divide 2 2 The second integer is x + 1 x = 25 2nd integer: 26

Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test 8. Carlie Jo is 8 years younger than Gina. Tuana is one year older than Gina. The sum of their ages is 29. a) Write a variable equation for the given information. Tuana is one year older than Gina Carlie Jo is 8 years younger than Gina The sum of their ages is 29 Assign variables: Let, g = Gina’s age , g – 8 = Carlie Jo’s age, g + 1 = Tuana’s age g + g – 8 + g + 1 = 29 Simplify 3g – 7 = 29 b) How old is each person? 3g – 7 = 29 Gina’s age is g Gina is 12 yrs old Add + 7 + 7 3g = 36 Carlie Jo is g – 8 Carlie Jo is 4 yrs old Divide 3 3 Tuana is g + 1 Tuana is 13 yrs old g = 12

Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test 9. Juanita has the same number of dimes as nickels. She has a total of $1.95. How much of each coin does she have? Let, d = # of dimes, Write an equation. n = # of nickels, .10d + .05n = 1.95 Since there is the same number of dimes as nickels, substitute n for d. .10n + .05n = 1.95 Multiply by 100 to eliminate decimal point 10n + 5n = 195 15n = 195 Combine 15 15 Divide n = 13 She has 13 of each coin.

Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test 10. Dwayne weighs two-thirds as much as his older sister. The sum of their weights is 90 lbs. How much does Dwayne weigh? Let, d = Dwayne’s weight, Write an equation. s = Sister’s weight, d + s = 90 Since Dwayne weighs two-thirds as much as his sister substitute s for d. 2 3 2 s + s = 90 Multiply by 3 to eliminate fraction 3 2s + 3s = 270 5s = 270 Combine 5 5 s = 54 Divide

Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test 10. Dwayne weighs two-thirds as much as his older sister. The sum of their weights is 90 lbs. How much does Dwayne weigh? sister = 54 pounds Do not let others distract you. Be responsible for your actions. Since Dwayne weighs two-thirds as much as his sister, multiply her weight by two-thirds to obtain Dwaynes weight. D = S 2 3 D = (54) 2 Substitute 3 D = 36 Dwayne weighs 36 pounds.