Word Problems — Speed/Distance/Age, Discount & Interest - Flashcards
Master essential numerical problem-solving skills through word problems involving speed, distance, time, age relationships, discount calculations, and simple interest. These concepts are fundamental for Philippine entrance exams and practical life applications.
Flashcards
What is the basic formula for calculating speed?
Answer
Speed = Distance ÷ Time. This fundamental formula helps solve problems where you need to find how fast something is moving. For example, if a jeepney travels 120 km in 3 hours, its speed is 120 ÷ 3 = 40 km/h.
How do you convert km/h to m/s?
Answer
Multiply by 5/18 or multiply by 1000 and divide by 3600. Example: 72 km/h = 72 × (5/18) = 20 m/s. This conversion is important for physics problems and standardized tests.
A bus travels 180 km in 4 hours going to Baguio, then returns in 3 hours. What is the average speed for the entire trip?
Answer
Average Speed = Total Distance ÷ Total Time = (180 + 180) ÷ (4 + 3) = 360 ÷ 7 = 51.43 km/h. Note: Don't just average the two speeds - use total distance over total time.
What is discount and how is it calculated?
Answer
Discount is the reduced amount from the original selling price. Formula: Discount = List Price - Selling Price. Discount % = (Discount ÷ List Price) × 100. Example: Item costs ₱1000, sold for ₱800. Discount = ₱200, Discount % = 20%.
A shirt originally costs ₱1,500 with a 25% discount. What is the selling price?
Answer
Method 1: Discount = 1500 × 0.25 = ₱375. Selling Price = 1500 - 375 = ₱1,125. Method 2: Selling Price = 1500 × (100% - 25%) = 1500 × 0.75 = ₱1,125.
What are the three types of discounts mentioned in business mathematics?
Answer
- Trade Discount - offered by distributor to retailer, not end customer. 2. Quantity Discount - given for buying in large quantities. 3. Promotional Discount - offered for new products or stock clearance.
What is Simple Interest and what is its formula?
Answer
Simple Interest is interest calculated only on the principal amount. Formula: I = P × r × t, where I = interest, P = principal, r = annual rate (as decimal), t = time in years. It's used in basic loans and savings calculations.
Find the simple interest on ₱50,000 at 6% per year for 3 years.
Answer
I = P × r × t = 50,000 × 0.06 × 3 = ₱9,000. The maturity value would be ₱50,000 + ₱9,000 = ₱59,000. This shows how money grows with simple interest over time.
How do you calculate the principal when given interest, rate, and time?
Answer
P = I ÷ (r × t). Example: If interest earned is ₱2,400 at 8% for 2 years, then P = 2,400 ÷ (0.08 × 2) = 2,400 ÷ 0.16 = ₱15,000.
What is the difference between Simple Interest and Compound Interest?
Answer
Simple Interest: calculated only on principal amount (I = Prt). Compound Interest: calculated on principal plus accumulated interest (F = P(1+r)^t). Compound interest grows exponentially while simple interest grows linearly.
Maria is 4 years older than Juan. In 6 years, Maria will be twice as old as Juan is now. How old is Juan currently?
Answer
Let Juan's current age = x. Maria's current age = x + 4. In 6 years, Maria = x + 4 + 6 = x + 10. Equation: x + 10 = 2x. Solving: 10 = x. Juan is currently 10 years old, Maria is 14 years old.
What are the key steps in solving age word problems?
Answer
- Assign variables to unknown ages. 2. Set up relationships for present, past, or future ages. 3. Create equations based on given conditions. 4. Solve algebraically. 5. Check your answer by substituting back. Remember: if present age is x, then n years ago = x-n, n years later = x+n.
A car travels the first 100 km at 50 km/h and the next 200 km at 75 km/h. What is the average speed?
Answer
Time1 = 100÷50 = 2 hours. Time2 = 200÷75 = 2.67 hours. Average Speed = Total Distance ÷ Total Time = (100+200) ÷ (2+2.67) = 300 ÷ 4.67 = 64.3 km/h.
What is the formula for Maturity Value in Simple Interest?
Answer
Maturity Value (F) = P + I or F = P(1 + rt), where P = principal, I = interest, r = rate, t = time. This represents the total amount received after the interest period ends.
How long will it take for ₱25,000 to earn ₱3,750 in simple interest at 5% per year?
Answer
t = I ÷ (P × r) = 3,750 ÷ (25,000 × 0.05) = 3,750 ÷ 1,250 = 3 years. This formula helps determine investment or loan duration.
A store offers a 15% discount on items over ₱2,000 and additional 5% for senior citizens. What does a senior citizen pay for a ₱3,000 item?
Answer
Step 1: Regular discount = 3,000 × 0.15 = ₱450. Price after discount = 3,000 - 450 = ₱2,550. Step 2: Senior discount = 2,550 × 0.05 = ₱127.50. Final price = 2,550 - 127.50 = ₱2,422.50.
What is Compound Interest and its basic formula?
Answer
Compound Interest is interest calculated on both principal and accumulated interest. Formula: F = P(1 + r)^t, where F = future value, P = principal, r = interest rate per period, t = number of periods. Interest = F - P.
Two trains start from opposite ends of a 480 km track. One travels at 60 km/h, the other at 40 km/h. When will they meet?
Answer
Combined speed = 60 + 40 = 100 km/h (approaching each other). Time to meet = 480 ÷ 100 = 4.8 hours. They meet 4 hours and 48 minutes after starting. Distance from first train's start = 60 × 4.8 = 288 km.
If a gadget's price drops from ₱8,000 to ₱6,400, what is the discount percentage?
Answer
Discount = 8,000 - 6,400 = ₱1,600. Discount % = (1,600 ÷ 8,000) × 100 = 0.2 × 100 = 20%. The price decreased by one-fifth of the original price.
Pedro borrowed ₱15,000 and paid ₱18,000 after 2 years. What was the simple interest rate?
Answer
Interest = 18,000 - 15,000 = ₱3,000. Rate = I ÷ (P × t) = 3,000 ÷ (15,000 × 2) = 3,000 ÷ 30,000 = 0.10 = 10% per year. This is the annual simple interest rate charged.
Diagrams
Word Problems Overview
Comprehensive overview of all word problem types covered in this chapter, showing the relationships between different concepts and their subcategories.
Speed Distance Time Problem Solving Process
Step-by-step flowchart for solving speed, distance, and time word problems, helping students systematically approach these problems.
Simple Interest Calculation Process
Systematic approach to solving simple interest problems, covering all possible scenarios and formula manipulations.