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### Unit 4: Lesson 6

Writing & solving proportions

# 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?
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?
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?
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?
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?
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?

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?
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

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?
candles

## Want to join the conversation?

• I dont know how to do ANY of this
• almost none of this was covered in the videos.
• and why dont i see any of this stuff in the viedos
• How do I even know what number to multiply by to get the percent?
• I liked math until now ):
• it's more complicated than in the videos.
• 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
• 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.