Word problems that need more than one step to solve
When One Proportion Isn't Enough
Some problems require you to solve a proportion first, then use that answer in a second calculation — a unit conversion, a subtraction, a comparison, or another proportion.
Examples
A car uses 3 gallons for 90 miles. Gas costs $4/gallon. How much does a 210-mile trip cost?
A factory makes 150 widgets in 2 hours. They work 8-hour shifts. How many widgets in a 5-day work week?
Step 1: Widgets per shift: 150/2 = x/8 → x = 600 widgets/shift
Step 2: Weekly: 600 × 5 = 3,000 widgets
Store A: 3 lb for $7.50. Store B: 5 lb for $11.50. You need 15 lb. How much do you save at the cheaper store?
Step 1: Store A unit price: $7.50/3 = $2.50/lb → 15 lb = $37.50
Step 2: Store B unit price: $11.50/5 = $2.30/lb → 15 lb = $34.50
Step 3: Savings: $37.50 − $34.50 = $3.00
Strategy for Multi-Step Problems
💡 Break it down:
1. Read the whole problem first
2. Identify what you ultimately need to find
3. Figure out what intermediate value you need first
4. Solve step by step — don't try to do it all at once
5. Check that your final answer makes sense in context
🎯 Practice Problems
1. A printer prints 40 pages in 5 minutes. How many pages in 1 hour?
A) 200
B) 320
C) 400
D) 480
2. A recipe serves 4 using 2 cups flour. Flour costs $3 per 5 cups. How much flour cost to serve 12?
A) $1.80
B) $3.00
C) $3.60
D) $6.00
3. Car A: 30 mpg. Car B: 25 mpg. Gas is $4/gallon. How much more does Car B cost for a 300-mile trip?
A) $8
B) $10
C) $12
D) $16
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🎯 Bonus Practice
1. A factory makes 200 items in 3 hours with 4 workers. How many items can 6 workers make in 9 hours?
A) 600
B) 900
C) 1,200
D) 1,800
2. Map scale: 1 inch = 20 miles. Two cities are 4.5 inches apart. A car goes 60 mph. How long is the drive?
A) 1 hour
B) 1.5 hours
C) 2 hours
D) 3 hours
3. Store sells 3 packs for $12. Each pack has 8 items. What is the cost per item?
A) $0.40
B) $0.50
C) $1.50
D) $4.00
4. A garden uses 5 gallons of water per 20 sq ft. Your garden is 8ft × 15ft. Water costs $0.01 per gallon. What is the weekly watering cost if you water 3 times a week?
A) $0.90
B) $1.50
C) $1.80
D) $2.40
5. Earning $15/hour, 8 hours/day, 5 days/week. How many weeks to earn $3,600?