MathIsimple

Lesson 7-3: Multi-Step Real-World Problems

Tackle complex real-world scenarios requiring multiple mathematical concepts and strategies.

Real-World
Multi-Step
Problem Solving
Complex
What You'll Learn
  • • Analyze complex real-world scenarios systematically
  • • Break down multi-step problems into manageable parts
  • • Choose appropriate mathematical strategies for different situations
  • • Integrate multiple math concepts in single problems
  • • Develop confidence in solving challenging problems
Problem-Solving Framework

The RIDE Method

R
Read & Understand
I
Identify & Plan
D
Do the Math
E
Evaluate & Check

Detailed Steps:

  1. Read: Read the problem carefully, identify key information
  2. Identify: Determine what you need to find, what operations to use
  3. Do: Work through the problem step by step, show all work
  4. Evaluate: Check your answer, make sure it makes sense
Complex Scenario 1: School Fundraiser

The Problem

A school is organizing a fundraiser to buy new playground equipment. They plan to sell cookies for $2.50 each and lemonade for $1.75 per cup. The school has 4 classes with 25 students each. Each student is expected to sell 3 cookies and 2 cups of lemonade. The playground equipment costs $1,200. Will they raise enough money? If not, how much more do they need to raise?

Solution Using RIDE Method

R - Read & Understand:

• 4 classes × 25 students = 100 students total

• Each student sells: 3 cookies + 2 cups lemonade

• Prices: $2.50 per cookie, $1.75 per cup

• Goal: $1,200 for equipment

I - Identify & Plan:

• Find total cookies and lemonade sold

• Calculate total revenue

• Compare to goal

D - Do the Math:

• Total cookies: 100 × 3 = 300 cookies

• Total lemonade: 100 × 2 = 200 cups

• Cookie revenue: 300 × $2.50 = $750

• Lemonade revenue: 200 × $1.75 = $350

• Total revenue: $750 + $350 = $1,100

E - Evaluate & Check:

• $1,100 < $1,200, so they need $100 more

• Answer: No, they need $100 more

Complex Scenario 2: Garden Project

The Problem

A community garden is 40 feet long and 30 feet wide. They want to plant vegetables in 3/4 of the area and flowers in the remaining area. The vegetable section will be divided into 12 equal plots. Each plot needs 2.5 pounds of fertilizer. Fertilizer costs $4.50 per pound. The flower section needs 1.25 pounds of fertilizer per square foot. What's the total cost for fertilizer?

Solution Using RIDE Method

R - Read & Understand:

• Garden: 40 ft × 30 ft = 1,200 sq ft total

• Vegetables: 3/4 of area, divided into 12 plots

• Flowers: 1/4 of area

• Fertilizer costs: $4.50 per pound

I - Identify & Plan:

• Find vegetable area and flower area

• Calculate fertilizer needed for each section

• Find total cost

D - Do the Math:

• Vegetable area: 1,200 × 3/4 = 900 sq ft

• Flower area: 1,200 × 1/4 = 300 sq ft

• Vegetable fertilizer: 12 plots × 2.5 lbs = 30 lbs

• Flower fertilizer: 300 × 1.25 = 375 lbs

• Total fertilizer: 30 + 375 = 405 lbs

• Total cost: 405 × $4.50 = $1,822.50

E - Evaluate & Check:

• $1,822.50 seems reasonable for a large garden

• Answer: $1,822.50

Complex Scenario 3: Travel Planning

The Problem

A family of 4 is planning a 5-day vacation. They'll drive 350 miles to their destination at 55 miles per hour, stay for 3 days, then drive back. Their car gets 25 miles per gallon and gas costs $3.20 per gallon. Hotel costs $120 per night. They budget $50 per person per day for food and activities. What's their total vacation cost?

Solution Using RIDE Method

R - Read & Understand:

• 4 people, 5 days total (2 travel + 3 stay)

• 350 miles each way = 700 miles total

• Car: 25 mpg, gas $3.20/gallon

• Hotel: $120/night for 3 nights

• Food/activities: $50/person/day

I - Identify & Plan:

• Calculate gas cost

• Calculate hotel cost

• Calculate food/activity cost

• Add all costs

D - Do the Math:

• Gas needed: 700 ÷ 25 = 28 gallons

• Gas cost: 28 × $3.20 = $89.60

• Hotel cost: 3 × $120 = $360

• Food/activities: 4 people × 5 days × $50 = $1,000

• Total cost: $89.60 + $360 + $1,000 = $1,449.60

E - Evaluate & Check:

• $1,449.60 for 4 people for 5 days seems reasonable

• Answer: $1,449.60

Strategy Selection Guide

When to Use Each Strategy

  • Draw a diagram: Geometry, spatial problems
  • Make a table: Comparing multiple options
  • Work backwards: When you know the end result
  • Use estimation: To check if answer is reasonable
  • Break into parts: Complex multi-step problems

Common Problem Types

  • Money problems: Budgeting, shopping, costs
  • Measurement problems: Area, volume, conversions
  • Rate problems: Speed, work, efficiency
  • Mixture problems: Combining different amounts
  • Comparison problems: Finding differences, ratios

Problem-Solving Tips

  • • Read the problem at least twice before starting
  • • Underline or highlight important information
  • • Draw pictures or diagrams when helpful
  • • Show all your work clearly
  • • Check your answer by working backwards
  • • Ask yourself: "Does this answer make sense?"
Practice Problems

Problem 1: School Field Trip

A school is planning a field trip for 3 classes of 28 students each. The bus costs $200, and each student pays $15 for admission. The school has $1,000 in the field trip fund. How much more money do they need? If they can't raise more money, how many students can go on the trip?

Your solution:

Problem 2: Pizza Party Planning

A pizza party for 20 people needs 2.5 slices per person. Each pizza has 8 slices and costs $12. They also need 3 drinks per person at $2.50 each. What's the total cost? If they have a budget of $200, how much money will be left over?

Your solution:

Problem 3: Sports Tournament

A basketball tournament has 8 teams. Each team plays every other team once. Each game lasts 1.5 hours, and there are 2 courts available. If games start at 9 AM and there's a 30-minute break between games, what time will the tournament end? If each team pays $50 to enter, how much money is collected?

Your solution:

Problem 4: Garden Design

A rectangular garden is 24 feet long and 18 feet wide. You want to plant flowers in 2/3 of the area and vegetables in the rest. The flower section will be divided into 6 equal beds. Each flower bed needs 1.5 pounds of fertilizer at $3.75 per pound. The vegetable section needs 2 pounds of fertilizer per square foot at $2.50 per pound. What's the total fertilizer cost?

Your solution: