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:
- parts gold yarn
- parts bronze yarn
- parts silver yarn
The magic carpet is made with a total of meters of yarn.
How much silver yarn is in the magic carpet?
Jasmine buys the magic carpet on sale for . Jasmine saved off the regular price.
What percent was the price of the magic carpet discounted?
Problem 2: Soccer
Joel is training for soccer season.
- On Monday, Joel exercises for minutes before school, and of that time is spent playing soccer.
- On Monday, Joel exercises for minutes after school, and of that time is spent playing soccer.
What is the total amount of time, in minutes, that Joel plays soccer on Monday?
Joel spends more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of minutes after school.
What percent of his time exercising after school did Joel spend playing soccer on Tuesday?
On Wednesday, Joel, who is right-footed, takes exactly of his practice shots on goal with his left foot. Joel takes shots with his left foot.
How many total shots on goal did Joel take on Wednesday?
Problem 3: Candles
A candle maker plans to make orange candles. She mixes wax to create a specific shade of orange. The ratio of each color in her mixture is shown below:
- parts red wax
- parts yellow wax
- parts white wax
The candle maker needs quart of orange wax for every candles.
How much yellow wax will the candle maker need to make all candles?
The candle maker makes a second batch of orange wax using the same ratio of yellow to red to white wax. She uses quarts of red wax in the second batch of orange wax.
How many total quarts is the second batch of orange wax?
The candles turn out great! So, the candle maker raises her normal price and sells candles for . She usually charges for candles.
How many dollars, per candle, did the candle maker raise her price?
The candle maker makes a total of orange candles. This is of all the candles she made this week.
How many candles did the candle maker make this week?
Want to join the conversation?
- 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)
- 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):
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)
- On the first question, how did you decide to multiply by 7.5? How was the problem set up? (part over whole)(12 votes)
- 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)
- im failing this class IDK HOW TO DO ANY OF THISSSS(10 votes)
- 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)