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## 7th grade

### Course: 7th grade > Unit 4

Lesson 6: Writing & solving proportions# Multi-step ratio and percent problems

CCSS.Math:

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

## 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.

## 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

## Want to join the conversation?

- I dont know how to do ANY of this(77 votes)
- almost none of this was covered in the videos.(78 votes)
- and why dont i see any of this stuff in the viedos(51 votes)
- I liked math until now ):(38 votes)
- How do I even know what number to multiply by to get the percent?(27 votes)
- it's more complicated than in the videos.(24 votes)
- im failing this class IDK HOW TO DO ANY OF THISSSS(18 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.(6 votes)

- On the first question, how did you decide to multiply by 7.5? How was the problem set up? (part over whole)(13 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!(3 votes)

- i did not understand some questions(14 votes)
- 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):

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)