Unit 2 Inequalities Practice Test - Mrs. Batdorf's Math Class



Unit 2 Inequalities Practice TestGeneration Date: 11/10/2019Generated By: Batdorf Suzanne 1. Clara wants to make some money during her summer vacations by selling handmade lace for $3.20 per yard. She has already earned $25.15. She wants to earn at least $110.75.How many more yards of lace does she need to sell to reach her goal? Select the inequality that includes the least number of yards of lace she can sell and still reach her goal.A.B.C.D.2. Ralphie's dad has a nutritionist who instructed him to consume less than 2,196 calories per day. He has already consumed 1,576 calories today and wants to eat some fruit bars that are 53 calories each. Which of the following inequalities could be used to solve for x, the number of fruit bars Ralphie's dad can eat without going over his calorie allotment? A.53x + 1,576 < 2,196B.53x < 1,576C.53x - 1,576 < 2,196D.53x < 2,1963. Michael has $1,051.37 in his checking account. He is going to spend $518.40 on a new television, and he will spend the rest on speakers that cost $46.00 each. Which of the following inequalities would determine the maximum number of speakers, x, Michael can buy without spending more money than he has in his account? A.$518.40 < $46.00x + $1,051.37B.$1,051.37 + $518.40 > $46.00 + xC.$46.00x + $518.40 < $1,051.37D.$518.40 + $46.00 + x < $1,051.374. Blaire needs more than 660 total points on assignments in her math class to get the grade she wants. She only has 220 points and needs to do some extra credit assignments that are worth 55 points each.How many extra credit assignments does Blaire need to complete in order to get the grade she wants? Select the inequality that includes the least number of extra credit assignments Blaire can complete and get the grade she wants in her math class. A.x > 7B.x > 220C.x > 8D.x > 4405. Kayla has a weekly budget of $685. She works at a clothing store and makes $315 per week, plus 20% commission on the merchandise she sells to her customers. The graph below models the dollar amount of merchandise Kayla sells each week. 1825183018351840184518501855186018651870187518801885Which of the following is the correct interpretation of the solution?A.Kayla can sell less than $1,850 to reach her weekly budget.B.Kayla needs to sell more than $1,850 to reach her weekly budget.C.Kayla needs to sell $1,850 or more to reach her weekly budget.D.Kayla can sell $1,850 or less to reach her weekly budget.6. Stella needs to fill a small pool with at least 35 gallons of water for her dog. There is currently gallons of water in the pool.If she is using a bucket that can hold gallons of water, how many buckets of water, x, will she need to reach her goal? Select the inequality that shows the minimum number of buckets needed to fill the pool. 7. Juanita works at a telemarketing company. She makes 12 sales calls per hour. Employees are encouraged to make more than 480 calls per week. Juanita has already made 168 calls this week. How many more hours, x, does Juanita need to work this week to reach the weekly goal of sales calls?Select the number line that includes the fewest number of hours Juanita can work and still reach her weekly goal of sales calls. A.22232425262728293031323334B.21222324252627282930313233C.21222324252627282930313233D.202122232425262728293031328. Ronny is selling coffee mugs for $4.00. So far, he has earned $344.00. Ronny needs to earn more than $432.00 in order to meet his sales goal. How many more coffee mugs, x, does Ronny need to sell in order to reach his sales goal?Select the number line that includes the fewest number of coffee mugs that Ronny can sell and still reach his sales goal. A.17181920212223242526272829B.17181920212223242526272829C.18192021222324252627282930D.161718192021222324252627289. A popular dance club allows 29 customers to enter per hour. The club has to keep their occupancy below 600 at any time during the day. Currently, the club has 339 customers. If none of the customers leave, how many more hours, x, can the club continue to accept new customers?Select the number line that includes the largest number of hours the club can continue to accept new customers without exceeding their occupancy. A.3456789101112131415B.567891011121314151617C.45678910111213141516D.4567891011121314151610. Gina is having a party and wants to spend less than $620. She has already spent $500. The only item left on her list is pizzas, which cost $15 each. How many pizzas, x, can she purchase and stay under her budget? Select the inequality that includes the largest number of pizzas she can purchase and still stay under her budget. A.x < 41B.x < 33C.x < 105D.x < 811. Tammy must run more than 82 miles total to reach her fitness goals. She has already run 34 miles and runs 6 miles per day. Which of the following inequalities could be used to solve for x, the number of days Tammy still needs to run to reach her fitness goals? A.34x > 34B.6x + 34 > 82C.6x > 82D.6x - 34 > 8212. Fran is limited to watching television for less than 14.4 hours per week. She has already watched 4.8 hours this week, and each show that she watches is 0.8 of an hour long.How many more shows can Fran finish watching this week? Select the inequality that includes the maximum number of shows Fran can finish and stay within her limitations. A.x < 12B.x < 10C.x < 8D.x < 1413. Sarah's youth group is selling candy bars for a fundraiser. The candy bars cost $1.50 each. To date, they have raised $900. Their goal is to raise more than $2,400. How many more candy bars, x, do they need to sell to reach their goal? Select the inequality that includes the smallest number of candy bars they can sell and still reach their goal. A.x > 1,000B.x > 1,500C.x > 2,800D.x > 1,80014. James is selling candy at a local marketplace. He needs to earn at least $200 to break even. He has already earned $11.25. If the price of one pound of candy is $2.50, how many more pounds of candy, x, does he have to sell to break even?Select the inequality that shows the minimum number of pounds he needs to sell to break even. A.102030405060708090100110120130B.102030405060708090100110120130C.102030405060708090100110120130D.10203040506070809010011012013015. James is selling candy at a local marketplace. He needs to earn at least $200 to break even. He has already earned $11.25. If the price of one pound of candy is $2.50, how many more pounds of candy, x, does he have to sell to break even?Select the inequality that shows the minimum number of pounds he needs to sell to break even. A.102030405060708090100110120130B.102030405060708090100110120130C.102030405060708090100110120130D.102030405060708090100110120130Answers1. A 2. A 3. C 4. C 5. C 6. D 7. C 8. B 9. C 10. D 11. B 12. A 13. A 14. B 15. A Explanations1. The situation can be modeled by a linear inequality of the form px + q ≥ r, where p is the cost per yard of lace, q is the amount of money already earned, and r is her goal.Set up an inequality and solve.Therefore, the inequality that includes the least number of yards of lace that she can sell and still reach her goal is x ≥ 26.75.2. The situation can be modeled by a linear inequality of the form px + q < r, where p is the number of calories per fruit bar, q is the number of calories Ralphie's dad has already consumed, and r is the total number of calories he is allowed per day.In this case, p = 53, q = 1,576, and r = 2,196.Therefore, the following inequality can be used to solve for x, the number of fruit bars Ralphie's dad can eat without going over his calorie allotment.53x + 1,576 < 2,1963. Michael cannot spend more money than he has in his account. Thus, the total of his spending must be less than or equal to $1,051.37. The symbol "<" is used to represent "less than or equal to".Now, look at Michael's planned expenses. He is going to spend $518.40 on a television. He is also going to spend $46.00 per speaker on as many speakers as he can afford. The number of speakers he can purchase is represented by x.In order to determine his total spending, multiply $46.00 by x, and then add $518.40 to the product.$46.00x + $518.40 < $1,051.374. In the given inequality, x represents the number of extra credit assignments Blaire needs to complete. Use opposite operations to isolate x.Therefore, the solution set for how many extra credit assignments Blaire needs to complete is x > 8.5. The graph contains a closed circle, which means $1,850 is included in the solution set, as well as all of the numbers shaded to the right, which are larger than $1,850. So, Kayla would need to sell merchandise worth $1,850 or more to reach her weekly budget. 6. The situation can be modeled by a linear inequality of the form px + q ≥ r, where p is the capacity of the bucket used to fill the pool, q is the amount of water currently in the pool, and r is the minimum amount of water needed for the pool.Set up an inequality and solve.Therefore, Stella needs to pour at least buckets of water into the pool to reach her goal. This inequality is shown on the number line below.7. The situation can be modeled by a linear inequality of the form px + q > r, where p is the number of sales calls per hour, q is the number of calls Juanita has already made this week, and r is the goal number of sales calls.Set up an inequality and solve.px + q>r12x + 168 >48012x>480 - 16812x>312x>26Therefore, Juanita needs to work more than 26 hours to reach the weekly goal of sales calls, as shown on the number line below.212223242526272829303132338. The situation can be modeled by a linear inequality of the form px + q > r, where p is the cost per coffee mug, q is the amount of money already earned, and r is his sales goal.Set up an inequality and solve.px + q>r$4.00x + $344.00 >$432.00$4.00x >$432.00 - $344.00$4.00x >$88.00x>22Therefore, Ronny needs to sell more than 22 coffee mugs to reach his sales goal, as shown on the number line below.171819202122232425262728299. The situation can be modeled by a linear inequality of the form px + q < r, where p is the average number of customers per hour, q is the number of customers already at the club, and r is the occupancy limit.Set up an inequality and solve.px + q<r29x + 339<60029x<600 - 33929x<261x<9Therefore, the club can continue to accept new customers for less than nine hours without exceeding their occupancy, as shown on the number line below.4567891011121314151610. The situation can be modeled by a linear inequality of the form px + q < r, where p is the cost per pizza, q is the amount of money already spent, and r is the party budget.Set up an inequality and solve.px + q<r$15x + $500<$620$15x<$620 - $500$15x<$120x<811. The situation can be modeled by a linear inequality of the form px + q > r, where p is the number of miles Tammy runs per day, q is the number of miles Tammy has already run, and r is the total number of miles she needs to run more than.In this case, p = 6, q = 34, and r = 82.Therefore, the following inequality can be used to solve for x, the number of days Tammy still needs to run to reach her fitness goals.6x + 34 > 8212. In the given inequality, x represents the number of shows Fran can finish watching. Use opposite operations to isolate x.Therefore, the solution set for how many more shows Fran can finish watching is x < 12.13. The situation can be modeled by a linear inequality of the form px + q > r, where p is the cost per candy bar, q is the amount of money already raised, and r is their fund raising goal.Set up an inequality and solve.px + q>r$1.50x + $900 >$2,400$1.50x>$2,400 - $900$1.50x>$1,500x>1,00014. The situation can be modeled by a linear inequality of the form px + q ≥ r, where p is the cost of one pound of candy, q is the amount he has already earned, and r is the minimum amount he needs to earn to break even.Set up an inequality and solve.Therefore, James needs to sell at least 75.5 pounds of candy to break even. This inequality is shown on the number line below.10203040506070809010011012013015. The situation can be modeled by a linear inequality of the form px + q ≥ r, where p is the cost of one pound of candy, q is the amount he has already earned, and r is the minimum amount he needs to earn to break even.Set up an inequality and solve.Therefore, James needs to sell at least 75.5 pounds of candy to break even. This inequality is shown on the number line below.102030405060708090100110120130 ................
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