Word Problems
Ummi uses a speaker to listen to a song. The song has a consistent beat. Ummi counts 11 beats in 5 seconds. What is the constant of proportionality for the relationship of beats to minutes?
What is 132 beats per minute?
Sample Work
Beats:Seconds
11:5
multiply ratio by 12
132:60
60 seconds=1 minute
COP stands for...
What is constant of proportionality?
The constant of proportionality in the following equation:
C=3.14D
What is 3.14?
Ms. Trubnikov finds a bubble recipe for a bubble solution that uses 1 cup of water, 0.25 cups of dish soap, and 1 tablespoon of glycerin. He uses two cups of dish soap. How much water should Josh use?
What is Josh should use 8 cups of water?
Sample Work
1/(1/4)=4 [constant of proportionality]
4x2=8 cups of water
A ratio that compares a quantity to a single unit of something else
What is a unit rate?
A new state policy requires a class size ratio of teachers to students in a classroom to be 1:23. If there are 23 teachers at a school, what is the maximum number of students the school can have?
What is 529 total students?
Sample work
Teachers:Students
1:23
Multiply ratio by 23
23:529
What is the constant of proportionality to go from hours to minutes?
What is 1/60?
Sample Work
Minutes to hours (Multiply by 60)
Hours to minutes (Multiply by 1/60)
Mr. Laird needs 4 goggles per table for his science class. Write an equation that demonstrates the relationship between the number of goggles, g, and the number of tables, t.
What is 4t=g
or
t=g/4
Ms. Odom and Ms. Hsu both drive 25 miles. Ms. Odom drives at a constant speed of 50 miles an hour. Ms. Hsu drives at a constant speed of 75 miles an hour. Who takes longer to drive the 25 miles? How much longer?
What is Ms. Odom takes 10 minutes or 1/6 hours longer?
Constant of Proportionality and Scale Factor are both examples of what?
What is a unit rate?
Jazmine and Darlene walk for the Lenox Breast Cancer Walk-A-Thon. Each girl walks for 10 minutes. Jazmine raises $5 per 1/3 minute while Darlene raises $8 per 1/2 minute. How much money will they raise together?
What is $310 raised together?
The constant of proportionality in one direction is 3/4. What is the constant of proportionality in the opposite direction?
What is 4/3?
Sample work
The COP in opposite direction is the reciprocal of the original COP
Ms. Odom drove 3.2 kilometers in 24 minutes. What is the constant of proportionality for the relationship in kilometers per hour? Write an equation to model this relationship between the number of kilometers, k, and the number of minutes, m.
What is 2m/15=k or 2m=15k (or equivalent)?
Sample Work
3.2/24= 2/15 (COP)
2m/15=k
Ms. Vines and Ms. Riggs start at opposite ends of a 55-mile bike trail. They start riding their bikes towards each other at the same time. After 3 hours, they meet. Ms. Vines rides 34 miles before they meet. What is Ms. Riggs average speed?
What is Ms. Vine's average speed is 7 miles per hour
Sample Work
55-34 -21 miles for Ms. Riggs
miles per hour = 21/3 = 7 miles per hour
Which variable is multiplied by the constant of proportionality.
(Hint: The COP is the coefficient of this variable)
What is X?
Ms. Telesford receives a $6 coupon for every 5 packs of index cards she purchases at Staples. How many packs of index cards must she purchase to get $30 off her next purchase?
What is 25 packs of index cards?
Sample Work
Coupons:Index Packs
6:5
Multiply by 5
30:25
Mr. Berry types 14/8 words per 1/2 minute. How many words can Mr. Berry type in 15 minutes?
What is 52.5 words per minute?
Sample work
Words:Minutes
14/8:1/2
28/8:1 minute
52.5:15 minutes
Given a table, how can you find the constant of proportionality if there isn't a value of 1 in either column of the table?
What is divide one set of numbers by the other set of numbers?
Ms. Miller mixes red and yellow paint in a ratio of 3:2 to create the perfect shade of pumpkin orange. If she uses a total of 70 grams of paint, how many grams of red and yellow paint will she need?
What is 42 grams of red paint and 28 grams of yellow paint.
Sample Work
Red:Yellow
3/5:2/5
?/70:?/70
70/5=14 therefore 3(14)=42 grams of red paint and 2(14)=28 grams of yellow paint.
Which coordinate contains a constant of proportionality?
A. (0,0)
B. (1,6)
C. (5,1)
D. (6,7)
What is B. (1,6)?