Exercises in problem solving
1. A company produces 450 gadgets each day. Due to increased demand, they plan to increase production by 12% every month. How many gadgets will the company produce after 3 months?
2. Sarah’s car uses 7.5 gallons of gas to travel 150 miles. If gas costs $3.80 per gallon, how much will Sarah spend on gas to travel 1,200 miles?
3. A rectangular garden has a length of 30 meters and a width of 18 meters. If the gardener wants to increase both the length and width by the same amount so the area becomes 900 square meters, by how many meters should each dimension be increased?
4. A water tank is shaped like a cylinder with a radius of 4 feet and a height of 10 feet. If water is drained at a rate of 2 cubic feet per minute, how long will it take to empty the tank?
5. A school plans a field trip for 120 students and 15 teachers. The bus company charges $500 for the first 50 passengers and $8 for each additional passenger. What is the total cost for the buses?
6. A store sells notebooks for $2.50 each and pens for $1.20 each. If a student buys 3 notebooks and some pens spending a total of $14.90, how many pens did the student buy?
7. A recipe calls for 3/4 cup of sugar to make 24 cookies. How much sugar is needed to make 60 cookies?
8. A cyclist travels 15 miles in 50 minutes. At the same rate, how far will the cyclist travel in 2 hours and 15 minutes?
9. A rectangular prism has dimensions 5 cm by 8 cm by 12 cm. If each dimension is doubled, by what factor does the volume increase?
10. A phone plan charges a fixed monthly fee of $25 plus $0.10 per minute of talk time. If a customer’s bill is $47.50, how many minutes did they use?
11. A company’s profit increases by 5% every quarter. If the profit was $80,000 last quarter, what will it be after 4 quarters?
12. A bridge is being constructed across a river 150 meters wide. If the bridge is built by connecting two ends with cables forming two right triangles, and the height of the towers is 60 meters, what is the length of each cable?
13. A container shaped like a cone has a height of 9 m and a base radius of 4 m. Find the volume of the container. (Use $$V = \frac{1}{3} \pi r^2 h$$)
14. A train leaves City A traveling at 60 mph. Two hours later, another train leaves City A traveling in the same direction at 75 mph. How long after the second train leaves will it catch up to the first train?
15. A farmer wants to fence a rectangular field using 540 meters of fencing. If the length is twice the width, what are the dimensions of the field?
16. A tank can be filled by pipe A in 3 hours and by pipe B in 6 hours. If both pipes are opened together, how long will it take to fill the tank?
17. A car depreciates in value by 15% each year. If the car is worth $20,000 now, what will be its value after 3 years?
18. A family plans a road trip of 540 miles. They drive for 3 hours at 60 mph and then for the rest of the trip at 75 mph. How long will the entire trip take?
19. A school fundraiser sells chocolate bars in packs of 12. If they need to raise at least $1,200 and each chocolate bar costs $2, how many packs must they sell?
20. A rectangular swimming pool is 25 meters long, 10 meters wide, and 2 meters deep. If the pool is filled at a rate of 500 liters per minute, how long will it take to fill the pool? (1 cubic meter = 1,000 liters)