Applications Using Whole Numbers

OPERATIONS & WORD PROBLEMS WITH RATIOS/PROPORTIONS

DIRECTIONS: Write answers with money in appropriate form. Reduce fractions/ratios to lowest terms. Round decimals to nearest hundredth/cent.

Do NOT use a calculator!

PART I: Write each ratio as a fraction in simplest form.

3 1 1) 25 inches to 135 inches 2) 4 feet to 8 feet 3) 20.5 pounds to 32.45 pounds 5 2

10 1 4) 9.3 grams to grams 5) 16 inches to 5 feet 6) 7 feet to 38 inches 3 2

1 1 1 7) 12 yards to 9.5 feet 8) 32.4 feet to 10 yards 9) 8 pounds to 8 ounces 4 4 4 10) 1800 pounds to 3 tons 11) 250 days to 1 year 12) 3 years to 120 weeks

1 13) 2 years to 30 months 14) 100 seconds to 10 minutes 2

15) Write each rate as a unit cost (cost per item). 1 a) 55 pounds for $39.16 b) $28 for 12 gallons c) 4 yards for $18.50 2

16) Write each rate as a unit rate. a) 350 miles in 6 hours (miles per hour) b) 45 gallons for 180 miles (miles per gallon) c) 6.5 feet in 13 minutes (feet per minute)

17) Desiree bought 5 feet of cotton fabric for $8.75. How much was the cost per foot?

18) The Buy Food Supermarket discards about 200 pounds of rotting vegetables and fruits each week. The Fresh Food Supermarket discards about 10,000 pounds of rotting vegetables and fruits each year. Which supermarket has the greater rate of discarded vegetables and fruits per day?

19) In a survey of 200,000 people, 135,000 of them indicated they would like to have a new football stadium built in their city. Write the ratio of the number of people who would like the stadium to the number of people surveyed.

20) Ten out of fifteen smokers surveyed want to stop smoking. Find the ratio of smokers who do not want to stop to the smokers surveyed.

21) The high school basketball team’s ratio of wins to losses (no ties) for last season was 24 to 18. Find the ratio of wins to games played last season. 23) In Lilith’s sculpting class there are twelve women and six men. Find the ratio of men in the class to the total number of people in the class.

24) A recent survey questioned if people would travel to a foreign country. The following were the responses; 135 people said yes, 104 people said no, and 26 people said maybe. Find the ratio of people who said yes to the total number of people surveyed.

25) On Monday, Harold decided to sell only two flavors of ice cream cones. He sold 235 chocolate ice cream cones and 355 vanilla ice cream cones. Find the ratio of chocolate ice cream cones to total number of cones sold on Monday.

26) The shoe store had 120 pairs of sneakers in stock on Monday. A shipment of sneakers was delivered to the store on Tuesday and there are now 210 pairs of sneakers in stock. Find the ratio of the number of pairs of sneakers in the shipment to the number of pairs of sneakers in stock on Tuesday.

27) A shipment of books has increased the value of inventory from $120,000 to $185,000. Find the ratio of the value of the inventory’s increase to the value before the shipment.

28) On Monday, a sports clothing store had 85 Oakland Raiders sweatshirts in stock. On Friday, the store had 50 sweatshirts in stock. Find the ratio of the decrease in Raiders sweatshirts to the sweatshirts in stock on Monday.

29) A landscaper had 100 5-pound bags of fertilizer. In the past week, he had 4 landscaping jobs in which he used 8 bags of fertilizer for each job. Find the ratio of bags of fertilizer used to the number of bags of fertilizer left.

PART II. Find each answer using proportions.

1) As inventory manager, Greg documented that for every 5 boxes of cereal sold, 3 boxes of instant oatmeal were sold. If Greg orders 300 boxes of cereal, how many boxes of instant oatmeal should he order?

2) Elementary school nurses know that for every 5 children with complaints of stomach ache, 3 children will vomit. If in one week in the month of January, 45 children visit the nurse’s office with a complaint of stomachache, how many of them vomited?

3) A survey of 220 mothers was conducted at a children’s department store. The ratio of mothers who preferred candy not be sold at the store to mothers who had no preference was 3 to 2. How many mothers preferred candy not be sold at the store?

4) The owner at a local pizzeria noticed that for every 10 plain pies sold, 7 pies with a topping were sold. A plain pie costs $10.99 and a pie with a topping costs $12.99. a) If in one day, 140 pies with a topping were sold, how many plain pies were sold? b) What was the total amount of income from both types of pies sold that day?

5) A local entertainment store sells DVD’s for $14.99 and video games for $12.29. Records of past sales indicate that for every 8 DVD’s sold, 5 video games are sold. In December, the manager expects to sell 400 DVD’s. How much income can the manager expect to earn in December in the sales of DVD’s and video games? 6) Trevor was charged $5 for every day his taxes were overdue. If Trevor’s taxes were overdue for 15 days, how much did Trevor pay in late fees?

7) Jose’s commission on selling a $250,000 home was $850. At that rate, how much commission would Jose get on a selling a $600,000 home?

8) Mrs. Tremble sells 3 knitted caps for every 4 knitted scarves. If she sold 450 knitted caps in one year, how many knitted scarves were sold?

9) If the scale on a map reads 1 inch = 5.5 miles, then what is the distance between two towns which measures 8 inches on the map?

10) On average, Evan jogs 2 miles in 6.5 minutes. How long will it take Evan if he jogs 7.5 miles?

11) A Beef Stroganoff recipe serving 5 people calls for 1 ½ cups of cream for every ½ cup of milk. Robert will be making Beef Stroganoff to serve 12 people. How many cups of cream and milk does Robert need?

12) If 5.5 pounds of potatoes cost $2.15, how much should 35 pounds of potatoes cost?

13) If one mile equals 5290 yards, how many yards are there in 12 miles?

14) At a park’s track, 12 laps is equivalent to 1 mile. Evelyn jogs 2 ½ miles, 4 days a week. How many laps does Evelyn jog in a year?

15) Johnny, the baker, needs 8 kilograms of chocolate chips to make 256 cookies. He has a 20-pound bag of chocolate chips in his pantry. Is that enough to make all the cookies? (1 kg = 2.2 lbs)

16) The local daycare likes to maintain a teacher to child ratio of 1 to 3. If in September the daycare will have 48 children in their care, how many teachers need to be hired?

17) It is estimated that for every 10 eighth-grader, 7 of them smoke at parties. If there are 150,000 eighth-graders in Cook County, how many of them may smoke at parties?

18) For every 10 people who join a gym, 6 of them will go at least three times a week. If 5000 people joined a gym in January, how many of them will go less than three times a week?

19) An intramural soccer team’s wins to losses ratio is 3 to 2. In the past two years, the team played 60 games (no ties). How many games did they win?

20) A business manager hires 2 supervisors for every 15 employees. If 24 supervisors were hired, how many employees are in the company?

21) Fifteen thousand pounds of grain are to be divided into two storage areas in the ratio of 5 to 3. How many pounds of grain will be put in each storage area?