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Back to Unit 6

Lesson 6-1: Multi-step Word Problems

Scenario: Business Planning - Learn to solve complex problems that require multiple mathematical concepts!

Duration: 70-85 minutesScenario: Business Planning

Learning Objectives

  • Break down complex problems into manageable steps
  • Apply multiple mathematical concepts to solve one problem
  • Use systematic approaches to problem solving
  • Apply business and project management math

Business Planning Scenario

The Problem

You're starting a small business selling handmade crafts. You need to plan your first month of operations. Here are the details: You can make 15 items per day, each item costs $8 to make, and you sell them for $18 each. You work 20 days per month. Your monthly expenses are: rent $500, utilities $150, and materials $1,200.

Business Challenge:
Calculate your monthly profit and determine if you need to adjust your pricing or production to break even.

Given Information

Production:

  • • 15 items per day
  • • 20 working days per month
  • • Cost per item: $8
  • • Selling price: $18

Monthly Expenses:

  • • Rent: $500
  • • Utilities: $150
  • • Materials: $1,200

Problem Solving Strategy

Step-by-Step Approach

Problem Solving Steps:

  1. 1. Identify what you need to find
  2. 2. List all given information
  3. 3. Break the problem into smaller parts
  4. 4. Solve each part step by step
  5. 5. Check your answer and make conclusions

What We Need to Find

  • • Total monthly production (items made)
  • • Total revenue (money from sales)
  • • Total production costs
  • • Total monthly expenses
  • • Monthly profit or loss
  • • Break-even analysis

Step-by-Step Solution

Step 1: Calculate Total Production

Items per day × Working days per month = Total production
15 × 20 = 300 items per month

Step 2: Calculate Total Revenue

Total items × Selling price per item = Total revenue
300 × $18 = $5,400

Step 3: Calculate Production Costs

Total items × Cost per item = Production costs
300 × $8 = $2,400

Step 4: Calculate Total Expenses

Rent + Utilities + Materials = Total expenses
$500 + $150 + $1,200 = $1,850

Step 5: Calculate Total Costs

Production costs + Monthly expenses = Total costs
$2,400 + $1,850 = $4,250

Step 6: Calculate Monthly Profit

Total revenue - Total costs = Monthly profit
$5,400 - $4,250 = $1,150

Analysis and Conclusions

Business Analysis

Good News: Your business is profitable! You're making $1,150 per month.

Profit Margin: $1,150 ÷ $5,400 = 21.3%

Break-even Point: You need to sell at least 236 items to break even

Recommendation: Your current pricing and production levels are working well!

Practice Problems

Problem 1: Restaurant Planning

A restaurant serves 120 customers per day at an average of $25 per customer. Daily costs are: food $800, labor $600, rent $200. Calculate the daily profit and monthly profit (30 days).

Your solution:

Problem 2: Event Planning

You're organizing a school dance. Tickets cost $15 each. You expect 200 students. Costs are: venue $800, DJ $300, decorations $200, refreshments $400. How much profit will you make, and what's the minimum number of tickets needed to break even?

Your analysis: