# Multi-step ratio and percent problems

CCSS Math: 7.RP.A.3
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 $\374$. Jasmine saved $\66$ 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 $20$ minutes before school, and $25\%$ of that time is spent playing soccer.
• On Monday, Joel exercises for $60$ minutes after school, and $40\%$ 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?
$\%$

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

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