Lesson 6-1: Multi-Step Word Problems

Scenario: Business Planning - Solve complex problems requiring multiple operations and strategic thinking!

Duration: 70-85 minutesScenario: Business Planning

Learning Objectives

Break down complex problems into manageable steps
Apply multiple operations in the correct sequence
Use problem-solving strategies effectively
Solve real-world business and financial problems

Business Planning Problem

School Fundraiser Planning

Your school is planning a fundraiser to buy new computers. You need to calculate the total cost, determine how many items to sell, and figure out the profit needed to reach your goal.

Problem Details:
• Goal: Raise $2,400 for new computers
• Items to sell: Cookies at $3 each, Brownies at $4 each
• Cost to make: Cookies cost $1.50 each, Brownies cost $2 each
• You want to sell 2/3 cookies and 1/3 brownies
• How many of each item do you need to sell to reach your goal?

Cookies
$3 each

Brownies
$4 each

Fundraiser items

Step-by-Step Solution

Step 1: Calculate profit per item

Cookie profit = $3.00 - $1.50 = $1.50 per cookie
Brownie profit = $4.00 - $2.00 = $2.00 per brownie

Step 2: Set up the equation

Let x = total number of items
Cookies: (2/3)x items × $1.50 = $1.00x
Brownies: (1/3)x items × $2.00 = $0.67x
Total profit: $1.00x + $0.67x = $1.67x = $2,400

Step 3: Solve for x

$1.67x = $2,400
x = $2,400 ÷ $1.67 = 1,437 items (rounded)

Step 4: Calculate individual quantities

Cookies: (2/3) × 1,437 = 958 cookies
Brownies: (1/3) × 1,437 = 479 brownies
Total: 958 + 479 = 1,437 items

Answer: You need to sell 958 cookies and 479 brownies to raise $2,400.

Problem-Solving Strategies

1. Read and Understand

• Read the problem carefully
• Identify what you need to find
• Highlight key information
• Draw a diagram if helpful

2. Plan Your Approach

• Break the problem into steps
• Decide which operations to use
• Set up equations or expressions
• Choose the best strategy

3. Solve Step by Step

• Work through each step carefully
• Show all your work
• Check calculations as you go
• Use estimation to verify

4. Check Your Answer

• Does the answer make sense?
• Work backwards to verify
• Check units and labels
• Consider if it's reasonable

Common Multi-Step Problem Types

Business & Finance

• Profit and loss calculations
• Budget planning
• Sales and discounts
• Investment returns

Measurement & Geometry

• Area and perimeter problems
• Volume calculations
• Scale and proportion
• Construction projects

Data & Statistics

• Survey analysis
• Probability calculations
• Statistical measures
• Data interpretation

Practice Problems

Problem 1

A store bought 120 shirts for $15 each. They sold 2/3 of them for $25 each and the rest for $20 each. What was their total profit?

Your solution:

Problem 2

A rectangular garden is 12 meters long and 8 meters wide. A path 2 meters wide runs around the outside. What is the area of the path?

Your solution:

← Back to Unit 6 Next: Problem-Solving Strategies →