# Multistep Ratio Problems

Related Topics:
Common Core for Mathematics
Lesson Plans and Worksheets for all Grades

Examples, solutions, worksheets, videos, and lessons to help Grade 7 students learn how to solve multi-step ratio problems.

### New York State Common Core Math Grade 7, Module 1, Lesson 14

Lesson 14 Student Outcomes

Students will solve multi-step ratio problems including fractional markdowns, markups, commissions, fees, etc.

Example 1: Bargains

A retail clothing store advertises the following sale: Shorts are 1/2 off the original price; pants are 1/3 off the original price, 1/4 off the original price (called the discount rate).

a. If a pair of shoes costs \$40 and is advertised at 1/4 off the original price, what is the sales price?

b. At Peter’s Pants Palace a pair of pants usually sells for \$33.00. If Peter advertises that the store is having 1/3 off sale, what is the sale price of Peter’s pants?

Example 2: Big Al’s Used Cars

A used car sales person receives a commission of 1/12 of the sales price of the car for each car he sells. What would the sales commission be on a car that sold for \$21,999?

Example 3: Tax Time

As part of a marketing ploy, some businesses mark up their prices before they advertise a sales event. Some companies use this practice as a way to entice customers into the store without sacrificing their profits.

A furniture store wants to host a sales event to improve their profit margin and to reduce their tax liability before their inventory is taxed at the end of the year.

How much profit will be business make on the sale of a couch that is marked-up by 1/3 and then sold at a 1/5 off discount if the original price is \$2400?

Example 4: Born to Ride

A motorcycle dealer paid a certain price for a motorcycle and marked it up by 1/5 of the price he paid. Later, he sold it for \$14,000 what is the original price?

Lesson Summary:

Discount price = original price – rate x original price OR (1 - rate) original price Commission = rate x total sales amount
Markup price = original price + rate x original price OR (1 + rate) original price.

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