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Unit 7 Advanced Worksheet

Mixed Problem Solving - Challenge Level - 20 Questions

Question 1: School fundraiser: Goal $500, raised $235. If 5 classes donate equally for the rest, how much per class?

Answer: $53

Needed: $500 - $235 = $265. Per class: $265 ÷ 5 = $53.

Question 2: Rectangle: length is 3 more than width. Perimeter is 30. Find the width.

Answer: 0

Try w=6: l=9, P=2(6+9)=30 ✓. Width is 6 feet.

Question 3: Fibonacci sequence: 1, 1, 2, 3, 5, 8, ___

Answer: 13

Each number = sum of previous two: 5 + 8 = 13.

Question 4: A baker starts with some cookies. After selling 15 and baking 12 more, has 30. How many at start?

Answer: 33

Work backwards: End 30. Before baking: 30-12=18. Before selling: 18+15=33 cookies.

Question 5: On a 3×3 grid, there are exactly 9 squares total.

Answer: False

False! 9 (1×1) + 4 (2×2) + 1 (3×3) = 14 squares total.

Question 6: How many handshakes if 5 people each shake hands once with everyone?

Answer: 0

P1: 4 handshakes, P2: 3 new, P3: 2 new, P4: 1 new = 4+3+2+1 = 10 total.

Question 7: Train: 8 cars, 45 seats/car, 20 empty seats. People on train: ___

Answer: 340

Total seats: 8 × 45 = 360. People: 360 - 20 = 340.

Question 8: Reading goal: 1,200 pages in 6 months. Read 350 in 2 months. Pages per month remaining to meet goal?

Answer: 212.5

Remaining: 1,200-350=850 pages. Months left: 4. Per month: 850÷4=212.5 pages.

Question 9: Painting room 12ft × 10ft. 1 gallon covers 100 sq ft, costs $35/gallon. Need how many gallons?

Answer: 0

Area: 12×10=120 sq ft. Need: 120÷100=1.2, so round up to 2 gallons.

Question 10: Area of rectangle is 24 sq ft. List one possible dimension pair: ___ × ___

Answer: 4 × 6

Factor pairs of 24: 1×24, 2×12, 3×8, 4×6. Any valid answer works!

Question 11: After rolling five 1's on a fair die, probability of rolling 1 next changes.

Answer: False

False! Each roll is independent. Still 1/6 chance regardless of past rolls.

Question 12: Sports team: 18 players, uniform $25, equipment $40 each. Total team cost?

Answer: $1,170

Per player: $25+$40=$65. Total: 18×$65=$1,170.

Question 13: Parking lot: 4 rows, each row has 2 more spaces than previous. Row 1 has 8. Total spaces?

Answer: 0

Rows: 8, 10, 12, 14. Total: 8+10+12+14=44 spaces.

Question 14: If n² = 64, then n = ___

Answer: 8

8 × 8 = 64, so n = 8. (Square root of 64)

Question 15: You buy 15 packs of 12 balloons. Need 240 for party. How many short or extra?

Answer: 60 short

Have: 15×12=180 balloons. Need: 240. Short by: 240-180=60 balloons.

Question 16: Bus schedule: buses every 15 min from 7:00 AM. Arrive 7:38 AM. Wait time?

Answer: 0

Buses at 7:00, 7:15, 7:30, 7:45. Arrive 7:38, next is 7:45. Wait: 7 minutes.

Question 17: School bus: picks up 12, 15, 8 students, then 10 get off. Students remaining: ___

Answer: 25

Picked up: 12+15+8=35. After drop-off: 35-10=25 students.

Question 18: Drawing a diagram always solves every type of problem.

Answer: False

False! Different problems need different strategies. Diagrams help some, not all.

Question 19: Garden: 8 rows, 7 plants/row, each needs 2L water weekly. Monthly water (4 weeks)?

Answer: 448 liters

Plants: 8×7=56. Weekly: 56×2=112L. Monthly: 112×4=448 liters.

Question 20: Sara reads 18 pages Mon, 22 Tue, 15 Wed. Book has 100 pages. Fraction left?

Answer: 0

Read: 18+22+15=55. Left: 100-55=45. Fraction: 45/100 = 9/20.

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