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Course: Operations and Algebraic Thinking 222-226 > Unit 1

Lesson 6: Writing & solving proportions
Math Content
Operations and Algebraic Thinking 222-226
Rates & proportional relationships
Writing & solving proportions
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Multi-step ratio and percent problems

Google Classroom
Use proportional relationships to solve multistep ratio and percent problems. Examples include simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Problem 1: Magic carpet

A magic carpet is made with three colors of yarn. The ratio of each color in the carpet is shown below:
  • 10 parts gold yarn
  • 7 parts bronze yarn
  • 3 parts silver yarn
Part A
The magic carpet is made with a total of 150 meters of yarn.
How much silver yarn is in the magic carpet?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
meters

Part B
Jasmine buys the magic carpet on sale for $374. Jasmine saved $66 off the regular price.
What percent was the price of the magic carpet discounted?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
%

Problem 2: Soccer

Joel is training for soccer season.
  • On Monday, Joel exercises for 20 minutes before school, and 25% of that time is spent playing soccer.
  • On Monday, Joel exercises for 60 minutes after school, and 40% of that time is spent playing soccer.
Part A
What is the total amount of time, in minutes, that Joel plays soccer on Monday?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
minutes

Part B
Joel spends 27 more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of 60 minutes after school.
What percent of his time exercising after school did Joel spend playing soccer on Tuesday?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
%

Part C
On Wednesday, Joel, who is right-footed, takes exactly 20% of his practice shots on goal with his left foot. Joel takes 14 shots with his left foot.
How many total shots on goal did Joel take on Wednesday?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
shots

Problem 3: Candles

A candle maker plans to make 30 orange candles. She mixes wax to create a specific shade of orange. The ratio of each color in her mixture is shown below:
  • 2 parts red wax
  • 5 parts yellow wax
  • 3 parts white wax
Part A
The candle maker needs 1 quart of orange wax for every 6 candles.
How much yellow wax will the candle maker need to make all 30 candles?
Choose 1 answer:

Part B
The candle maker makes a second batch of orange wax using the same ratio of yellow to red to white wax. She uses 7 quarts of red wax in the second batch of orange wax.
How many total quarts is the second batch of orange wax?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
quarts

Part C
The candles turn out great! So, the candle maker raises her normal price and sells 5 candles for $27. She usually charges $14.25 for 3 candles.
How many dollars, per candle, did the candle maker raise her price?
$
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Part D
The candle maker makes a total of 45 orange candles. This is 30% of all the candles she made this week.
How many candles did the candle maker make this week?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
candles

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