City Planning Challenge
You're part of a team planning a new neighborhood in your city. This involves making important decisions about land use, infrastructure, and community services. You'll need to use all your math skills to analyze data, calculate costs, and make recommendations that will affect thousands of people.
Calculate areas, costs, and optimal layouts for different land uses
Design roads, utilities, and services using geometric calculations
Analyze population data and plan schools, parks, and facilities
You have 120 acres of land to develop. City regulations require: 40% residential, 25% commercial, 20% parks, and 15% roads/utilities. Residential land sells for $50,000 per acre, commercial for $80,000 per acre. Parks cost $15,000 per acre to develop. What's the total revenue and cost for this development?
Determine how many acres go to each land use type.
Residential: 120 × 0.40 = 48 acres
Commercial: 120 × 0.25 = 30 acres
Parks: 120 × 0.20 = 24 acres
Roads/Utilities: 120 × 0.15 = 18 acres
Find revenue from selling residential and commercial land.
Residential revenue = 48 × $50,000 = $2,400,000
Commercial revenue = 30 × $80,000 = $2,400,000
Total revenue = $2,400,000 + $2,400,000 = $4,800,000
Find the cost to develop parks and infrastructure.
Park development cost = 24 × $15,000 = $360,000
Road/utility cost = 18 × $25,000 = $450,000
Total development cost = $360,000 + $450,000 = $810,000
Find the net profit after subtracting development costs.
Net profit = $4,800,000 - $810,000 = $3,990,000
Total revenue: $4,800,000
Development cost: $810,000
Net profit: $3,990,000
You need to design a road network connecting all areas. The main road is 2.5 miles long and 40 feet wide. Side roads are 1.2 miles long and 24 feet wide. If asphalt costs $85 per square yard, and 1 mile = 1,760 yards, what's the total cost for paving all roads?
Convert all measurements to yards for consistent units.
Main road: 2.5 miles × 1,760 yards/mile = 4,400 yards long
Main road width: 40 feet ÷ 3 feet/yard = 13.33 yards wide
Side roads: 1.2 miles × 1,760 yards/mile = 2,112 yards long
Side road width: 24 feet ÷ 3 feet/yard = 8 yards wide
Find the area of each type of road.
Main road area = 4,400 × 13.33 = 58,652 square yards
Side road area = 2,112 × 8 = 16,896 square yards
Total road area = 58,652 + 16,896 = 75,548 square yards
Find the total cost to pave all roads.
Total paving cost = 75,548 × $85 = $6,421,580
The total cost for paving all roads is $6,421,580.
The new neighborhood will have 1,200 families. City standards require: 1 school per 400 families, 1 park per 300 families, and 1 library per 600 families. Each school costs $8.5 million, each park costs $2.3 million, and each library costs $4.7 million. What's the total cost for community services?
Determine how many of each type of facility are needed.
Schools needed = 1,200 ÷ 400 = 3 schools
Parks needed = 1,200 ÷ 300 = 4 parks
Libraries needed = 1,200 ÷ 600 = 2 libraries
Find the cost for each type of facility.
School cost = 3 × $8,500,000 = $25,500,000
Park cost = 4 × $2,300,000 = $9,200,000
Library cost = 2 × $4,700,000 = $9,400,000
Add up all facility costs.
Total cost = $25,500,000 + $9,200,000 + $9,400,000 = $44,100,000
Find the average cost per family for community services.
Cost per family = $44,100,000 ÷ 1,200 families = $36,750 per family
Total cost for community services: $44,100,000
Cost per family: $36,750
A new development will remove 3/8 of a 240-acre forest. The remaining forest can absorb 0.4 tons of CO₂ per acre per year. If the city produces 1,200 tons of CO₂ per year, what percentage of the city's CO₂ can the remaining forest absorb?
A fire station needs to serve a 5-mile radius. The new neighborhood is 3.2 miles from the nearest station. If response time is 1.5 minutes per mile, and the maximum acceptable response time is 8 minutes, do you need a new fire station?
The new development will create 450 jobs. Each job generates $2,800 in monthly spending. If 60% of this spending stays in the local economy, and the local economy has a multiplier effect of 1.4, what's the total monthly economic impact?
You've successfully applied all the math concepts you've learned throughout 5th grade to solve complex, real-world problems. You now have the skills to:
You've mastered all the essential 5th grade math concepts and can now apply them to solve real-world problems. You're ready for 6th grade math and beyond!