Equivalent Ratios Problems
Unit Rate Problems
Unit Price: What's the better deal?
Conversions
Name That Ratio
100
A class has a student to teacher ratio of 6:2. Name an equivalent ratio to this ratio.
Answer: Multiply or divide both sides of the ratio by the same number.
Examples: 6:2 multiplied by 2 on both sides --> 12:4
6:2 divided by 2 on both sides--> 3:1
12:4 = 6:2 = 3:1
100
Find the unit rate for typed words per minute:
360 typed words for every 6 minutes
Answer: 60 words
360 div 60 = 6
100
The best deal or a better buy means that the unit price is the ______________.
Answer: Lowest amount of money or cheapest!
100
What are the two methods we learned to solve conversion problems?
Answer: Dimensional Analysis and Equivalent Ratios or Tables
100
What is the ratio of gray marbles to blue marbles in the picture below?
Answer: 16 gray marbles to 28 blue marbles
200
Shelter A has a ratio of cats to dog of 10:8
Shelter B has a ratio of cats to dogs of 4:3
Is both shelters had 20 cats, which shelter would have more dogs?
Answer: Shelter A
Shelter A: 10 cats to 8 dogs = 20 cats to 16 dogs
*(Multiply both sides by 2 to get to 20 cats)
Shelter B: 4 cats to 3 dogs = 20 cats to 15 dogs
*(Multiply both sides by 5 to get to 20 cats)
16 dogs >15 dogs
200
Find the unit rate per hour:
60 miles in 8 hours
Answer: 7.5 miles per 1 hour
60 divided by 8 = 7.5
200
Naruto can buy 3 bowls of ramen for $15.00 or 5 bowls of ramen for $20.00.
Which is the better buy?
Answer: 5 bowls for $20.00
Unit price for 3 bowls for 15 = 1 bowl for $5
Unit price for 5 bowls for 20 = 1 bowl for $4
$5 > $4, therefore 5 bowls is a better deal
200
Jack has 24 quarts of water. How many gallons does he have?
Conversion Factor: 1 gallon = 4 quarts
Answer: 6 gallons
24 div 4 =6
200
Using the picture below name of the ratio for the following:
100pts: Number of pears to total number of fruit
100pts: Number of apples to the number of pears
Answer:
Number of pears to total number of fruit = 3:9
Number of apples to number of pears = 6:3
300
Liam is using 18 black tiles and 12 white tiles to design a section of a garage floor.
100 points: Name the ratio of black tiles to total number of tiles in the design.
200 points: If there are 90 total tiles in the design, how many black and white tiles would there be according to the ratio?
Answer: Ratio is 18 black tiles to 30 total tiles.
There would be 54 black tiles and 36 white tiles if there was 90 total tiles.
18:30 ---- x3---> 54 black tiles to 90 total tiles
90 total tiles - 54 black tiles = 36 white tiles.
300
In 1 hour, 25 cars pass through a tunnel. At the same rate, how long would it take 100 cars to pass though the tunnel?
Answer: 4 hours
1 hour for 25 cars = 4 hours for 100 cars
300
Beth can buy package A of 6 binders for $4.02 or package B for 10 binders for $6.20.
Which is the best deal on binders?
Answer: Package B
Unit Price A: $4.02 divided by 6 = $0.67 per binder
Unit Price B:$6.20 divided by 10 = $0.62 per binder
0.62<0.65, Therefore package B is the better buy.
300
Lewis is 6 feet tall. How many inches is that?
Conversion factor: 12 inches = 1 foot
Answer: 72 inches
6 times 12 = 72
300
A box of color pencils has 2 blue pencils, 3 purple pencils and 4 green pencils. What is the ratio of blue pencils to purple pencils?
Extra 50 points --> Write the ratio three different forms.
Answer:
2:3, 2 to 3, or 2/3
400
Bradley decides to include 4 pages of photos for every 20 pages in his new book. If the book is 200 pages long, how many photographs will there be?
Answer:40 pages of photos
4 photos to 20 pages = 40 photos to 200 pages
(Multiply both sides by 10 to get equivalent ratios)
400
Fiona walks at a rate of 12 miles for 2 hours. At this rate how far would Fiona walk in 5 hours?
Answer: She would would 30 miles in 5 hours.
Unit Rate: 12 divided by 2 = 6 miles in 1 hour
In 5 hours, 6 x 5 = 30 miles walked.
400
Store A is selling 5 pizzas for $51.60.
Store B is selling 3 pizza for $30.12
What is the better deal for pizza?
Bonus 50 points: How money do you save per pizza?
Answer:
Unit Price Store A: $51.60 divided by 5 = $10.32 per pizza
Unit Price Store B: $30.12 divided by 3 = $10.04
10.32>10.04 Therefore Store B is a better deal by $0.28 (10.32 -10.04 = 0.28)
400
There are 3.65 liters of liquid in a bucket. How many milliliters of liquid is in the bucket?
Extra 100 points: What is the conversion factor for liters to milliliters?
Answer: 3650 milliliters
Conversion factor: 1 liter = 1000 milliliters
3.65 times 1000 = 3650
400
Here are some ordered pairs on a line: (2,4) (8,16) (12,24)
150 points: Write the ratios that you would plot on a graph.
150 points: Using your words, describes how I would graph each of the ratios.
100 points: Name another ratio and ordered pair that would be on the line with an x coordinate of 3.
Answers:
(2,4) --> 2:4 graph by going right 2 up 4
(8,16) --> 8:16 graph by going right 8 up 16
(12,24) --> 12:24 graph by going right 12 up 24
3:6 or 3/6 or 3 to 6 --> (3, 6) is an equivalent ratio and therefore on the line!
500
Greg makes 3 out of 5 free throws.
Courtney makes 7 out of 10 free throws.
Daniel makes 16 out of 20 free throws.
Who is the best free throw shooter? Use equivalent ratios to justify your answer.
Answer: Daniel is the best free throw shooter
Compare all ratios to 20 shoots!
Greg: 3:5 = 12:20 (times both sides by 4)
Courtney: 7:10 = 14:20 (times both sides by 2)
Daniel: 16:20 (already out of 20 did not change)
16 > 12 and 14 therefore Daniel is the best!
500
A machine can make 340 headphones in 8 hours. If the machine was left on for 10 hours, how many headphones would it create?
Answer: 425 headphones
Unit Rate: 340 divided by 8 = 42.5 headphones per hour
Machine on for 10 hours: 42.5 x 10 = 425 headphones for 10 hours
500
Two companies print books.
Company A will make 4,000 copies for $32,560
Company B will make 5,000 copies for $43,750
Which company gives a better deal for printing?
Answer: Company A
Company A Unit Price: $8.14 per book
32,560 divided by 4,000 = 8.14
Company B Unit Price: $8.75 per book
43,750 divided by 5000 = 8.75
8.14<8.75 therefore Company A has a better buy!
500
A bowling ball weighs an average of 10 pounds. What is the weight of the bowling ball in both kilograms and grams?
Conversion Factors:
1 lb is about 0.45kg 1 kg = 1000 grams
Answer: 4.5 kg and 4500 grams is about 10 pounds
0.45 kg x 10 pounds = 4.5 kg
4.5kg x 1000 grams = 4500 grams
500
Using the picture below name of the ratio for the following:
250 points: Number of apples to total number of fruit. Show the ratio in three different forms.
250 points: Number of blueberries to bananas. Show the ratio in three different forms.
Answer:
Apples to total fruit:
10:16, 10/16, 10 apples to 16 total fruit
Blueberries to bananas:
0:6, 0/6, 0 blueberries to 6 bananas