Name______
Example 1: Write the ratio that represents the situations below.
Total / Girls / BoysSwim Club / 40 / 24 / 16
Soccer Club / 30 / 12 / 18
- Compare girl soccer players to boy soccer players ______
- Compare girl swimmers to girl soccer players______
- Compare all soccer players to all swimmers______
Ratios can be simplified to equivalent ratios just like fractions.
4 to 2 would be equivalent to ______
8:4 would be equivalent to ______
would be equivalent to ______
A unit rate is a rate with a denominator of 1.
For example,
I can drive 120 miles in 2 hours can be expressed as:
How many miles can I drive in 1 hour? This is the unit rate.
Let’s Practice:
Fill in the rate and unit rate in the chart below for each situation.
Situation / Unit RateRun 10 miles in 2 hours
Earn $100 in 8 hours
Potatoes cost $2.25 for 5 pounds
Type 120 words in 3 minutes
Swim 400 meters in 160 seconds
The Main Street florist sells 2 dozen roses for $ 24.60. The Flowers for You Florist sells 6 roses for $7.50. Find the unit rate for each florist. Which florist has the lower cost per rose?
Which is the better buy per unit?
Bananas / 8 pounds for $2.72 / 5 pounds for $1.45Toilet Paper / 3 rolls for $2.04 / 9 rolls for $6.30
Diet Coke / 12 cans for $4.80 / 15 cans for $6.30
Turkey / ½ of a pound for $2.29 / 2 pounds for $9.10
Cheese / 2 pounds for $6.98 / 5 pounds for $16.50
Name______
Solve the word problems below. Show all of your work!
1) There have been 22 days in February. Of those days, 16 have been sunny. What is the ratio of sunny days to not so sunny days in simplest form? / 2) A baseball team won 9 of 16 games. What is the ratio of wins to losses?3) A soccer team played 32 games and won 20. Find the ratio of games won to games lost and simplify. / 4) You earn $54 for 4 hours of work. What is the unit rate? (How much do you get for 1 hour)
5) In the word BALLOONS, the ratio of vowels to consonants is? / 6) Which is the faster speed, 165 miles in 2.5 hours or 258 miles in 4 hours?
7) A pet store has 8 cats, 12 dogs, and 3 rabbits. The ratio 8:23 compares:
(1) dogs to cats (2) cats to dogs
(3) rabbits to cats (4) cats to all animals / 8) A vase contains 16 roses, 10 carnations, and 14 daisies. Write each ratio in lowest terms.
______a. roses to daisies
______b. carnations to all flowers
______c. daisies to roses and carnations
Unit Rate
$2680 for 5 tickets
16 cities in 4 days
9856 miles traveled, 4 travelers
11,076 pounds of luggage, 213 passengers
27 suitcases, 9 travelers
$6324 in tips, 62 skycaps
3335 passengers, 29 planes
966 miles traveled in 3 hours
4832 hot dogs, 2416 travelers
110 crew members, 22 planes
A ratio in word problems such a 3:5 is set up as two separate variables of 3x and 5x.
Example 1: Two numbers are in the ratio of 4:3. Their sum is 70. Find the numbers.Example 2: Two people weigh 288 pounds all together. The ratio of their weights is 4:5. How much does the heavier person weigh?
Example 3: Two numbers are in the ratio of 5:3. Their sum is 160. Find the numbers.
1) An inheritance of $54,000 is divided between Latasha, Linda, and Lori. If the ratio is 3 to 4 to 5, respectively, how much will each person receive?
2) Sterling silver is made of an alloy of silver and copper in the ratio of 37:3. If the mass of a sterling silver ingot is 600 grams, how much silver does it contain?
3) At the Phoenix Surfboard Company, $306,000 in profits was made last year. This profit was shared by the four partners in the ratio 3:3:5:7. Find out how much each partner made.
How much more money did the partner with the largest share make than one of the partners with the smallest share?
1) Julio makes $29.75 for 5 hours of work. How much does he make per hour?
How much will he earn for 30 hours of work at the same pay rate? / 2) A choir has 16 members, of which there are 10 female singers. What is the ratio of males to females in the choir?
3) In a math class there are 18 boys and 12 girls. What is the ratio, in reduced form, of the number of boys to the total number in the class? / 4) Chloe and Janet both agree to invest some of their monies. The ratio of Chloe’s investment to Janet’s investment is 8:5. If together they invested $14,300, how much did each person invest?
5)The profits in a business are to be shared by the three partners in the ratio of 3:2:5. The profit for the year was $176,500. Determine the number of dollars each partner is to receive.
AProportionis an equation that states that two ratios are equal.
“a is to b as c is to d”
a and d are theextremes of theProportion
b and c are themeans of the Proportion
State whether each sentence below is a proportion (write yes or no).
______a) ______c)
______b) ______d)
Are the ratios equal?
1) , / 2) , / 3) ,4) 5 to 3, 10 to 6 / 5) , / 6) ,
You can also solve proportions algebraically.
For example, you can solve for x in the proportion:
- Cross multiply:
- Go through the steps for solving an equation to solve for x:
Let’s Practice!
Solve for x in the proportions below:
1) / 2)3) / 4)
Proportion Word Problems
1)A man takes 7.5 hours to read a 375 page book. How many hours will it take him to read a 500 page book at the same rate?
2)You need 2 cups of sugar for every 5 cups of flour for a cookie recipe. If you use 12 cups of flour, how much sugar would you need?
3)A truck can travel 232 miles on 14.5 gallons of gasoline. How many gallons would the truck need to travel 400 miles?
Solve for x to make a true proportion. Show all your work.
1) / 2) / 3)4) If three servings of candy have 240 calories, how many calories are in 5 servings? / 5) On a map, 2 inches represent 50 miles. If two cites are 9 inches apart, how many miles are there between the two cities? / 6) A factory gets 8 defective parts for every 200 parts it manufactures. If the factory manufactures 2300 parts in one month, how many parts will be free of defects?
7)The ratio of the weight of an object on Jupiter to its weight on Earth is 8 to 3. How much would a 123 pound person weigh on Jupiter?
8)Tom worked 9 hours and earned $85.50. At the same rate of pay, if he works 15 hours next week, how much money should Tom earn next week?
1) / 2)
3) / 4)
5) / 6)
7) / 8)
9)
Determine the unit rate for each situation. (HINT: UNIT RATE MEANS HOW MUCH FOR 1)
1) 36 students, 4 tablesThe question you are trying to answer is: How many students at 1 table? / 2) 6696 buttons, 372 students
The question you are trying to answer is: How many buttons for 1 student / 3) 924 pieces of chalk, 6 chalk boards
The question you are trying to answer is: How many pieces of chalk per chalk board?
Solve the following word problems. Show all your work.
4) a. It took Julie 54 minutes to run 6 miles. Write a ratio to represent this situationb. How many minutes does it take Julie to run 1 mile (the unit rate)?
c. How long would it take Julie to run a full marathon, 26.2 miles? (Hint: Set up a proportion use information in part a to set this up)
5) A restaurant made $545 in profit from selling 109 hamburgers. If they sold 53 hamburgers during lunch, what was their profit?(Hint: Set up a proportion and cross multiply).
Solve each proportion for x. Show all your work. CROSS MULTIPLY!
6) / 7)8) / 9)
10) Two numbers are in the ratio of 7:8. If the sum of the numbers is 180, find the value of the larger number.
Hint: Set up 7x:8x…Sum means add….equation must equal 180. / 11) In a restaurant the ratio of waiters to tables is 2 to7. If there are 10 waiters, how many tables are there in the restaurant?
Hint: set up the proportion
12) If 6 lbs of flour cost $4.00, how many pounds of flour can be purchased for $14?
Hint: set up a proportion…..what are the 2 quantities you are working with? / 13) If 100 grams of ice cream contain 15 grams of fat, how many grams of fat are in 260 grams of ice cream?
Hint: set up a proportion…..what are the 2 quantities you are working with?
Answer Box:
1) 9 students/1 table.2) 18 buttons/ 1 student
3) 154 chalk/1 board / 4) a)
b) 9 min for 1 mile
c) 235.8 min / 5)
x=$265 / 6) 4(x-4) = 56
x = 18
7) 9(5x+5)=3(9x-3)
45x+45=27x-9
x = / 8) x = 2.28 / 9) 30 = 10 ( x – 3 )
x = 6 / 10) 7x + 8x = 180
x = 12
Larger number= 96
11)
x = 35 / 12)
x = 21 / 13)
x = 39