HFCC Math Lab NAT 06 Solving Word Problems Can you solve general word problems requiring multiple steps? Example 1: A student was required to spend about 60 hours during the semester to complete a project online. He has completed 36 hours of work online and there are 10 days left in the semester. What this is the average number of hours he needs to spend daily in order to achieve his goal? 1. Find the number of hours left to complete the online project. 60 36 24 hours left 2. Find the average hours per day to achieve his goal. 24 hours 2.4 10 days hrs /day The student needs to spend an average of 2.4 hrs /day to achieve his goal. Example 2: Sandra is making equal student loan payments. In the last three months, equal payments were deducted from her checking account. Her account had a starting balance of $1245 and an ending balance of $816. What was the amount of each payment? 1. Find the total amount she paid. $1245 $816 $429 She paid $429 in the last three months. 2. Find the amount of each payment. $429 $143 per payment 3 payments Each payment was $143 per month. Can you solve word problems involving proportion? Example 3: A health official wants to know how many people in Canton contracted a severe cold last winter. The health worker surveys 300 people, 125 of whom reported having a severe cold. If 45,000 people live in Canton, about how many people had a severe cold? Step1: Set up a proportion. Let x represent the number of people in Canton with a severe cold. 125 colds : 300 people :: x colds : 45,000 people Revised 5/2011 1
125 colds x colds 300 people 45, 000 people 300x 125(45, 000) 300x 5, 625,000 300 300 x 18, 750 Approximately 18,750 people in Canton had a severe cold last winter. Example 4: A nurse gives 300 mg of Aspinozin to a 75 kg patient. At this rate, how much Aspinozin should a 55 kg patient receive? Step 1: Set up a proportion. Let x represent the amount of Aspinozin a 55 kg patient receives. x mg : 55 kg :: 300 mg : 75 kg x mg 300 mg 55 kg 75 kg 75x 300 55 75x 16,500 75x 16,500 75 75 x 220 A 55 kg patient receives 220 mg of Aspinozin. Example 5: A woman received a bottle of perfume as a present. The bottle contains ¾ liters of perfume. How many milliliters is this? Round to the nearest milliliter. (1 L 1,000 ml) Step 1: Set up a proportion. Let x represent the amount of perfume in milliliters. 3 x ml : l :: 1,000 ml : 1 l 4 x ml 1,000 ml l 1 l 3 4 3 x 1 1000 4 x 750 The bottle contains 750 ml of perfume. Revised 5/2011 2
Can you solve problems involving percents? Example 6: A medication was tested on 5,000 patients. Of those 5,000 people, 2,756 had no side effects. What percent of people had no side effects? Round to the nearest whole percent. Step 1: Set up the percent proportion. Let x represent the percent of people with no side effects. x people : 100 total :: 2,756 people : 5,000 total x people 2,756 people 100 total 5, 000 total 5, 000x 100(2, 756) 5, 000x 275, 600 5,000 5,000 x 55 55% of the people had no side effects. Example 7: Last month 360 babies were born at a hospital. Of the births, 55% were boys. How many girls were born last month? Step 1: Set up the percent proportion. Let x represent the number of boys that were born last month. 55 boys : 100 total :: xboys : 360 total 55 boys x boys 100 total 360 total 100x 55(360) 100x 19,800 100 100 x 198 198 boys were born last month Step 3: Find the number of girls born last month. 360 198 162 girls Therefore, 162 girls were born last month. Revised 5/2011 3
Example 8. Sarah is a nurse earning a $56,000 salary. She received a 2.5% cost-of-living raise, what is the change in her salary and what is her new salary? Step 1: Set up the percent proportion. 2.5 part : 100 total :: x part : 56,000 total 2.5 part x part 100 total 56, 000 total 100x 2.5(56, 000) 100x 140, 000 100 100 x 1400 Sarah s salary increased $1, 400. Step 3: Find Sarah s new salary. $56, 000+ 1, 400 $57, 400. Therefore, Sarah s new salary is $57, 400. Exercises: Ex 1. A worker is filling out his time sheet. He worked 7 hours on Monday, 6 hours on Tuesday, 8 hours and 30 minutes on Wednesday, 5 hours 15 minutes on Thursday, and 7 hours and 45 minutes on Friday. If he earns $16.75 per hour, what will be his total earnings for the week? Ex 2. A hospital night staff consists of 20 registered nurses, 80 unlicensed assistants, three receptionists, and 37 physicians. During a snow day, 75% of the staff showed up to work. How many people were working that night? Ex 3. An intravenous fluid is infused at a rate of 3.5 milliliter per minute. How many milliliters are infused per hour? Ex 4. A patient was told to cut back on his intake of caffeine. The patient usually has five 8-oz cups of coffee and tea per day. If the doctor told him to cut back by 45%, how many ounces of coffee can the patient have each day? Ex 5. According to the nutrition label, one large egg contains 6 grams of protein. This is 10% of the daily value of protein. Express this percent as a fraction. Ex 6. A lab technician mixed 56 milliliters of alcohol with 144 milliliters of water to make a solution. What percent of the solution was alcohol? Revised 5/2011 4
Ex 7. A patient s medication was increased by another 40 milligrams. If the original medication was 180 milligrams, what was the percent increase in the medication? Ex 8. Twenty-five grams of sugar are dissolved in 150 grams of water. What is the percent of sugar in the solution? Round your answer to the nearest whole percent. Ex 9. You answered 85% of the 60 questions on an exam correctly. How many questions did you answer correctly? Ex 10. An 800 g solution of Kool-Aid contains 780 g of water. What is the mass percent of solute in this solution? Ex 11. A chemistry teacher has 4 liters of sodium hydroxide. To perform an experiment, each student needs 70 ml of solution hydroxide. Will the teacher have enough solution for 200 students? Ex 12. You had $100 to spend. You went to the first store and spent $23.55 and then you spent $31.80 at another store. How much money do you have left? Ex 13. An 8-oz non-fat Caramel Macchiato at Starbucks has 90 calories. How many calories are there in a 12-oz non fat Caramel Macchiato? Ex 14. There are 102 milligrams of cholesterol in a 4-ounce serving of skinless chicken. How much cholesterol is in 14 ounces of skinless chicken? Ex 15. A store purchased 34 cases of eggs, each case has contains 18 cartons. If 12 eggs are in each carton, how many eggs are there? Ex 16. Lisa purchased 20 thermometers for $28 each and 4 blood pressure monitors for $34.00 each. If she had $746.00 in her expense account before the purchase, how much is left in her account? Ex 17. In a class of 32 students, 18 students have jobs. What percent of the students do not have jobs? Ex 18. Rebecca purchased a blood pressure monitor for $68.50. The store then charged her 6% sales tax. How much sales tax did Rebecca pay? Ex 19. Christy s credit card charges 14% annual simple interest. She was charged $56.60 in simple interest last month. What was her balance? Round to the nearest dollar amount. Ex 20. Kathy is a registered nurse making $23.50 an hour. She will be asked to take a pay cut of 3% next month. What will be her hourly earnings next month? Ex 21. There are 6 qt of blood in an average-sized man. Express this amount to the nearest tenth of a liter. Revised 5/2011 5
Ex 22. The average level of cholesterol in U.S. children is 160 mg per 100 ml of blood. Express this ratio in terms of grams per liter. Ex 23. A nurse must administer a 5-ml dose of a drug per day to a patient. If there is 1.4 L of this drug on hand, will it last the patient for 150 days? Ex 24. Vitamin C commonly comes in pills with a strength of 500 mg. How many of these pills will an adult need to take daily if he wants a dosage of 14 grams per week? Ex 25. A 212-pound man joined a weight-loss program and lost 63.6 lbs. What percent of his original weight did he lose? Ex 26. In a recent year, about 27% of the 880 thousand American doctors were female. How many female doctors were there, to the nearest thousand? Revised 5/2011 6
Solutions to the odd-numbered exercises and answers to the even-numbered exercises 1. Total number of hours 7+ 6+ 8.5+ 5.25+ 7.75 34.5 Total earnings (34.5)($16.75) $577.88 The worker earned $577.88 for the week. 2. 105 people were working that night. 3. 3.5 ml : 1 min :: x ml : 60 min 3.5ml x ml 1 min 60 min 1 x 60 3.5 x 210 ml 210 ml of intravenous fluid are infused per hour. 4. The patient can have 22 ounces of coffee each day. 5. 10 1 10% 10% is equivalent to the fraction 1 100 10 10. 6. The solution is 28% alcohol. 7. 40 : 180 :: x : 100 40 x 180 100 180x 40(100) 180x 4, 000 180 180 x 22% (rounded to the nearest whole percent) 8. The solution is 14% sugar. 9. 85 : 100 :: x : 60 85 x 100 60 100x 60(85) 100 x 5,100 x 51 100 100 You answered 51 questions correctly. 10. There is 2.5% percent solute in the solution. Revised 5/2011 7
11. 70 ml : 1 student :: x : 200 students 70 ml x ml 1 student 200 students 1 x 70 200 x 14,000 The teacher needs 14,000 ml of the solution. Convert to liters: x l 1 l 14000 ml 1000 ml 1, 000x 14, 000(1) 1, 000 x 14, 000 1,000 1,000 x 14 liters The teacher does not have enough solution for 20 students, because 14 liters is greater than 4 liters. 12. You have $44.65 left. 13. 90 calories : 8 oz :: x calories : 12 oz 90 calories x calories 8 oz 12 oz 8 x 90 12 8 x 1, 080 x 135 8 8 There are 135 calories in a 12 oz non-fat Caramel Macchiato. 14. There is 357 mg of cholesterol in 14 ounces of skinless chicken 15. 18 cartons : 1 case :: x cartons : 34 cases 18 cartons x cartons 1case 34 cases 1 x 18 34 x 612 cartons The store purchased 612 cartons of eggs. Now find the total number of eggs: x eggs : 612 cartons :: 12 eggs : 1 carton x eggs 12 eggs 612 cartons 1 carton 1 x 12 612 x 7,344 There are total of 7,344 eggs. 16. Lisa has $50 left in her account. Revised 5/2011 8
17. 32 18 14 students without jobs 14 : 32 :: x : 100 14 x 32 100 32x 14(100) 32 x 1, 400 x 44 32 32 44% of the students do not have jobs. 18. Rebecca paid $4.11 in sales tax. 19. 14: 100 total :: 56.60 : x total 14 56.60 100 x 14x 100(56.60) 14 x 5, 660 x 404 14 14 Her balance is $404 to the nearest dollar. 20. Her hourly earnings next month will be $22.80. 21. x l : 6 qt :: 1 l : 1.057 qt [1 liter 1.057 qt] x l 1 l 6 qt 1.057 qt 1.057x 6(1) 1.057 x 6 x 5.7 1.057 1.057 5.7 liters is equivalent to 6 quarts. 22. The average level of cholesterol in U. S. children is 1.6 grams per liter of blood. Revised 5/2011 9
23. x ml : 150 days :: 5 ml : 1 day x ml 5 ml 150 days 1 day 1 x 5 150 x 750 ml The patient will receive a total of 750 ml of the drug over the 150 days. Convert to liters: xl 1 l 750 ml 1, 000 ml 1000x 750 1, 000 x 750 x 0.75 1,000 1,000 Yes, the drug will last 150 days because 0.75 liters is less than 1.4 liters. 24. The adult needs to take 4 pills a day. 25. 63.6 lbs : 212 total lbs :: x : 100 total 63.6 lbs x 212 lbs 100 212x 63.6(100) 212x 6,360 212 212 x 30 The man lost 30% of his original weight. 26. There are 238 thousand female doctors Revised 5/2011 10