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

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 $\mathrm{}374$. Jasmine saved $\mathrm{}66$ off the regular price.
What percent was the price of the magic carpet discounted?
$\mathrm{%}$

Problem 2: Soccer

Joel is training for soccer season.
• On Monday, Joel exercises for $20$ minutes before school, and $25\mathrm{%}$ of that time is spent playing soccer.
• On Monday, Joel exercises for $60$ minutes after school, and $40\mathrm{%}$ 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?
$\mathrm{%}$

Part C
On Wednesday, Joel, who is right-footed, takes exactly $20\mathrm{%}$ 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 $\mathrm{}27$. She usually charges $\mathrm{}14.25$ for $3$ candles.
How many dollars, per candle, did the candle maker raise her price?
$\mathrm{}$

Part D
The candle maker makes a total of $45$ orange candles. This is $30\mathrm{%}$ of all the candles she made this week.
How many candles did the candle maker make this week?
candles

Want to join the conversation?

• almost none of this was covered in the videos.
• I agree I don't know like have the stuff in this thing!
• I dont know how to do ANY of this
• and why dont i see any of this stuff in the viedos
• I liked math until now ):
• I agree
(1 vote)
• it's more complicated than in the videos.
• How do I even know what number to multiply by to get the percent?
• devide the percent by 100
(1 vote)
• why wasn't an example like this done on the video. I don't understand this at all