Basics
Unit Rates
Proportional
Equations
Scale Factor
100
How do you find the unit rate?
y/x
100
What is the cost per pencil if there are 20 pencils for $4.00?
4.00/20 = $0.20 per 1 pencil
100
Is the table proportional? x y 5 12 7 15 9 17 11 20
NO!
100
iTunes is starting a new service. The service allows customers to download 25 songs for $12. Write an equation to find the total cost for any given number of songs.
COP-- $12/25 songs=0.48 y=.48x
100
How is scale factor calculated by?
Scaled measurement / Original measurement
200
What are all the names for unit rate?
Unit Rate Constant of Proportionality Scale Factor
200
Mrs. Larson has 16 homework papers and 14 exit tickets to return. Mr. Parris has 64 homework papers and 60 exit tickets to return. Are they proportional?
Mrs. Larson -- 16 hw/14 et = 1.14 hw per 1 et Mr. Parris -- 64 hw/60 et = 1.07 hw per 1 et NO!
200
Every year the 7th graders go on a field trip to a local museum. In 2011, the school paid $1260 for 84 students, in 2012 they paid $1050 for 70 students, and in 2013 they paid $1395 for 93 students. Is the cost per student proportional?
1260/84=15 1050/70=15 1395/93=15 YES
200
Ella walks 5/7 of a mile in 40 minutes. Write an equation to determine how far she walks, in hours.
COP -- 5/7 / 40/60 = 1.07 miles per hour y=1.07x
200
When calculating scale what is the x value? What is the y value?
x=original y=scaled
300
If two ratios are proportional, what has to be the same?
The unit rate
300
Blue Palm charges by the ounce for frozen yogurt and toppings. If each person in Mr. Fletcher's family gets frozen yogurt, what is the cost per ounce? Weight (ounces) 12.5 10 5 8 Cost ($) 5 4 2 3.20
$5/12.5 ounces= $0.40 per ounce
300
A recent study claims that for every 5 text messages a boy sends, a girl sends 7 text messages. Is the relationship between the number of text messages sent by boys proportional to the number of text messages sent by a girl?
YES! For every 5 messages a boy sends a girl sends 7
300
Alicia is driving to Spokane. She uses 3.5 gallons of gas to travel 60 miles. If Spokane is 125 miles away, how much gas will she use? Assume the rate will be constant. Round to the nearest whole number.
COP -- 60/3.5=17 y=17x 125=17x y=125/17 y=7 gallons
300
A rectangular pool in your friend's yard is 150 ft x 400 ft. What are the dimensions if they were to create a scaled model using a scale factor of 1/600?
8 x 3
400
How do you determine if a graph is proportional or not?
Straight line (linear) Goes through the origin
400
Alicia is driving to Spokane. She used 5.2 gallons of gas and traveled 125 miles. How many miles did she travel per gallon of gas?
125 miles/5.2 gallons=24 miles per gallon
400
Josh and Joseph have new jobs. Josh is Joseph's boss. In their first year, Josh will be paid $15 per hour and Joseph is paid $8 per hour. They have been told that they will receive a $2 per hour raise every year they work for the company. Does the constant of proportionality change every year?
YES
400
Netflix is starting a new service. The service allows subscribers to rent 3 new movies each month for $5. Write an equation to represent the cost of any number of movies rented.
COP -- $5/3=$1.67 y=1.67x
400
A drawing of a surfboard in a catalog shows its length as 8 9/4 inches. Find the actual length of the surfboard if 1/2 inch length on the drawing corresponds to 3/8 foot of actual length?
The actual is 6 1/3 feet long.
500
What is the equation format that we use to solve ratio problems? What do the letters stand for?
y=kx y is the y value k is the constant of proportionality x is the x value
500
It is a Saturday morning and Jeremy has discovered he has a leak coming from the water heater in his attic. Since plumbers charge extra to come out on weekends, Jeremy is planning to use buckets to catch the dripping water. He places a bucket under the drip and steps outside wot walk the dog. In half an hour the bucket is 1/5 of the way full. How full will the bucket be in one hour?
1/5 bucket/ 1/2 hour = 2/5 bucket per 1 hour
500
iTunes is starting a new service. The service allows customers to download 25 songs for $12. The constant of proportionality is what?
$12/25 songs = $0.48 per song
500
When a song is sold by an online music store, the store takes some of the money and the singer gets the rest. If the sales of the music store is $200, the singer gets $40. Write an equation to represent this situation.
COP -- $200/$40=$5 y=5x
500
A toy company is redesigning their packaging for model cars. The graphic design team needs to take the old image, which is 2 inches long and resize it it so that 1/2 inch on the old packaging represents 1/3 inch on the new package. Find the length of the image on the new package.
Scale factor: 1/3 / 1/2 = 2/3 2/3 * 2= 1 1/3 inches
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