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Multi-step ratio and percent problems

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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
meters

Part B
Jasmine buys the magic carpet on sale for dollar sign, 374. Jasmine saved dollar sign, 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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent

Problem 2: Soccer

Joel is training for soccer season.
  • On Monday, Joel exercises for 20 minutes before school, and 25, percent of that time is spent playing soccer.
  • On Monday, Joel exercises for 60 minutes after school, and 40, percent 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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent

Part C
On Wednesday, Joel, who is right-footed, takes exactly 20, percent 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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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:
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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
quarts

Part C
The candles turn out great! So, the candle maker raises her normal price and sells 5 candles for dollar sign, 27. She usually charges dollar sign, 14, point, 25 for 3 candles.
How many dollars, per candle, did the candle maker raise her price?
dollar sign
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Part D
The candle maker makes a total of 45 orange candles. This is 30, percent 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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
candles

Want to join the conversation?

  • blobby green style avatar for user Makena Mittendorf
    I dont know how to do ANY of this
    (63 votes)
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  • leafers sapling style avatar for user Jackson Hodges
    almost none of this was covered in the videos.
    (62 votes)
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  • blobby green style avatar for user mr4039924
    and why dont i see any of this stuff in the viedos
    (38 votes)
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  • starky sapling style avatar for user Jocelyn Vargas
    How do I even know what number to multiply by to get the percent?
    (22 votes)
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  • blobby green style avatar for user HenryG
    I liked math until now ):
    (26 votes)
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  • blobby green style avatar for user Kendrick H.
    it's more complicated than in the videos.
    (17 votes)
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  • blobby green style avatar for user aseelaftab123
    In problem no 3 part b how the answer would be 35 quarts plz explain the last step further as I am not getting from whom to multiply to get that value? Please illustrate
    (7 votes)
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    • leaf green style avatar for user John
      I didn't fully understand the explanation at first either.

      The first thing that helped me figure it out was to figure out what proportion of the whole the red wax accounted for. There are 10 total parts, and the red wax accounts for 2 of them, or 2/10, or 1/5, or .2 or 20% of the whole. However you want to think about it.

      If the candlemaker used 7 quarts of red wax in her second batch, 7 quarts must be 1/5 of the total quarts used in the new batch. A way you could express this mathematically would be (if t=the total number of candles made in the new batch):
      7=1/5t

      If you solve the equation by multiplying both sides by 5/1, you'll find that the candle maker made 35 candles in her new batch. What's nice in this case is that you have the opportunity to check your answer - you can just multiply 1/5 x 35 to make sure you get 7.
      (12 votes)
  • blobby green style avatar for user Dawneen Christian
    On the first question, how did you decide to multiply by 7.5? How was the problem set up? (part over whole)
    (12 votes)
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    • aqualine ultimate style avatar for user Zentua :3
      I think it is because in order to get '20' to '150' you need to multiply 7.5 by 20. In other words, 150/20 is 7.5 so we already have half of the ratio (The answer must be an equivalent ratio to 3 : 20). __:150. To get the last half of the answer, we must multiply 7.5 by 3 because we already found out that 150/20 is 7.5. 3 x 7.5 is 22.5 so the answer is 22.5 : 150. Hope this helps!
      (1 vote)
  • starky sapling style avatar for user Emory :P
    im failing this class IDK HOW TO DO ANY OF THISSSS
    (10 votes)
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    • duskpin sapling style avatar for user Kittenz
      Here's an example that might help you!
      lets say that Joey exercised 60 min on Monday after school, and 40% of it was playing soccer. So on Monday, he practiced 60(.40)=24 minutes playing soccer.
      He played 27 more (adding) minutes playing soccer on Tuesday after school. Adding 24+27=51.
      (3 votes)
  • blobby green style avatar for user josephg0665
    i did not understand some questions
    (9 votes)
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