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Name: ________________________ Class: ___________________ Date: __________ ID: A Unit 3 Benchmark Review #1 1. Miranda wants to buy 8 pencils. She has a $12 gift card and a coupon for $10 off. Which inequality models the price, x, for how many pencils she can afford. a. 8x 10 12 b. 10 8x 12 c. 8x 10 12 d. 10 8x 12 8. Solve 24 3y 33 9. Use the number line to represent the solution to the inequality 4x 6 5? 2. Select all the expressions equivalent to 10x 40? a. b. c. d. 10. mAOC 125 mDOF 48 What is the measure of COD? –5 (2x 8) 5(2x 8) 2 ( –5x + 20) –2 ( 5x + 40) 3. Select all expressions that are equivalent to 9x 4(8x 6) 3(x 8) a. 23x 3x 2 b. 20x 48 c. 20x 24 24 d. 12x 32x 24 24 4. You bought one team shirt and one hat for each of the 8 players on a team. Each team shirt costs $13.50 and the total cost was $206.00. Write an equation that you could use to find the cost of each hat (x ). 11. Consider this figure. What is the value of x 5. Solve the equation 7.4 6m 5.2 6. You bought one appetizer and one main course for each of the 12 guests at a party. Each appetizer costs $8.50 and the total cost was $171.00. Write an equation that you could use to find the cost of each main course (x ). 12. Write an expression equivalent to 2.5x 2.8 2.4x 3.5 7. Jiovani is graphic artist. He charges an initial fee of $86.25, plus $90 per hour. Jiovani earned $558.75 on a job. a) Write an equation that models this situation where h represents the number of hours he worked. b) How long did the job take? 1 Name: ________________________ ID: A 13. 19. Write an expression equivalent to (2x 5) (x 12) with as few terms as possible 20. A bike is 7 miles away from school and is driven away at a rate of 14 miles per hour. Which equation could you use to find how many hours, x , it will take for the bike to be 30 miles away from school. a. 7 14x 30 b. 7x 14 30 c. 7 14x 30 d. 7 14x 30 AOB measures ______ An angle complementary to AOE measures ______ An angle supplementary to COD measures ______ An angle vertical to COD measures ______ 21. Which number line shows the solution to the inequality 6x 2 5? 14. Solve for x and find the measure of XOY a. b. 15. Solve for x and find the measure of XOY c. d. 16. Consider this figure. What is the value of x 22. You buy 3 items and pay $7.75 for shipping. What was your cost per item if you paid a total of $57.25? 17. Is this work correct? If not, in which step contains the first error? 4(2x 4 11) 5(12 8x 1) Step 1 4(2x 7) 5(11 8x) Step 2 8x 28 55 40x Step 3 48x 83 18. Solve the equation 15.6 5m 4.9 2 ID: A Unit 3 Benchmark Review #1 Answer Section 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. C A, C B, D 8(x 13.5) 206.00 OR 8x 108 206.00 OR 108 8x 206.00 OR equivalent m 2.1 12(x 8.5) 171.00 OR 12x 102 171.00 OR 102 12x 171.00 OR equivalent a) 86.25 90h 558.75 OR 90h 86.25 558.75 b) 5.25 hours y 3 55 x 31 0.1x 6.3 AOB measures 49 An angle complementary to AOE measures 49 An angle supplementary to COD measures 139 An angle vertical to COD measures 41 x=23 mXOY=99° x=23 mXOY=103° x 37 Step 2 m 4.1 x 17 A C $16.50 per item 1