Math Grade 8 Word Problem Set 1 Worksheet Answer Key

Math Grade 8 Word Problem Set 1 Worksheet Answer Key

Word problems are an essential component of eighth-grade mathematics, helping students apply abstract concepts to real-world situations. This comprehensive answer key provides detailed solutions to a variety of challenging word problems that cover key topics in the eighth-grade curriculum. Each solution includes step-by-step explanations to help students understand the problem-solving process and develop critical thinking skills.

Types of Word Problems in Grade 8 Math

Eighth-grade word problems typically involve several mathematical concepts:

• Algebraic equations and expressions
• Geometric concepts and calculations
• Ratios, proportions, and percentages
• Probability and statistics
• Linear functions and graphing
• Systems of equations

Understanding these different categories helps students approach each problem with the appropriate strategies and mathematical tools Less friction, more output..

Sample Word Problems with Detailed Solutions

Problem 1: Algebraic Equation

Problem: Sarah is twice as old as her brother. In five years, the sum of their ages will be 28. How old are they now?

Solution:

Let's define variables:

• Let S = Sarah's current age
• Let B = Brother's current age

From the problem, we can create two equations:

1. S = 2B (Sarah is twice as old as her brother)
2. (S + 5) + (B + 5) = 28 (In five years, the sum of their ages will be 28)

Now, let's solve the system of equations:

First, simplify equation 2: S + B + 10 = 28 S + B = 18

Substitute equation 1 into this simplified equation: 2B + B = 18 3B = 18 B = 6

Now find Sarah's age using equation 1: S = 2B = 2(6) = 12

Answer: Sarah is currently 12 years old, and her brother is 6 years old Simple, but easy to overlook..

Problem 2: Geometry

Problem: A rectangular garden has a length that is 4 meters longer than its width. If the area of the garden is 60 square meters, what are the dimensions of the garden?

Solution:

Let's define variables:

• Let W = width of the garden (in meters)
• Let L = length of the garden (in meters)

From the problem, we can create two equations:

1. L = W + 4 (length is 4 meters longer than width)
2. L × W = 60 (area is 60 square meters)

Substitute equation 1 into equation 2: (W + 4) × W = 60 W² + 4W = 60 W² + 4W - 60 = 0

Now, we need to solve this quadratic equation. We can factor it: (W + 10)(W - 6) = 0

This gives us two possible solutions for W: W = -10 or W = 6

Since width cannot be negative, W = 6 meters.

Now find L using equation 1: L = 6 + 4 = 10 meters

Answer: The garden is 10 meters long and 6 meters wide Worth knowing..

Problem 3: Ratio and Proportion

Problem: A recipe calls for flour and sugar in the ratio of 5:3. If you use 8 cups of sugar, how much flour should you use?

Solution:

We know that the ratio of flour to sugar is 5:3. Let's set up a proportion:

5/3 = F/8

Where F is the number of cups of flour needed.

To solve for F, we can cross-multiply: 5 × 8 = 3 × F 40 = 3F F = 40/3 F = 13 1/3

Answer: You should use 13 1/3 cups of flour.

Problem 4: Percentage

Problem: A store is having a sale where all items are 25% off. If a jacket originally costs $80, what is the sale price? How much will you save?

Solution:

First, calculate the discount amount: Discount = Original Price × Discount Percentage Discount = $80 × 25% = $80 × 0.25 = $20

Now, calculate the sale price: Sale Price = Original Price - Discount Sale Price = $80 - $20 = $60

Answer: The sale price of the jacket is $60, and you will save $20 Simple, but easy to overlook..

Problem 5: Probability

Problem: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If you randomly select one marble, what is the probability that it is blue or green?

Solution:

First, find the total number of marbles: Total marbles = 5 (red) + 3 (blue) + 2 (green) = 10 marbles

Now, find the number of favorable outcomes (blue or green): Blue marbles = 3 Green marbles = 2 Total favorable outcomes = 3 + 2 = 5

Probability = Number of favorable outcomes ÷ Total number of outcomes Probability = 5 ÷ 10 = 0.5 or 50%

Answer: The probability of selecting a blue or green marble is 50%.

Problem 6: Linear Functions

Problem: A phone company charges a monthly fee of $30 plus $0.10 per minute of talk time. If your bill for last month was $50, how many minutes did you talk?

Solution:

Let's define variables:

• Let m = number of minutes talked
• Let C = total cost

The cost function can be written as: C = 30 + 0.10m

We know that C = $50, so: 50 = 30 + 0.10m

Subtract 30 from both sides: 20 = 0.10m

Divide both sides by 0.10: m = 20 ÷ 0.10 = 200

Answer: You talked for 200 minutes last month.

Common Mistakes and How to Avoid Them

When solving word problems, students often make these mistakes:

1. Not reading the problem carefully - Always read the problem at least twice to understand what is being asked Simple, but easy to overlook..

2. Using the wrong operation - Identify whether you need to add, subtract, multiply, or divide based on the problem context.

3. Ignoring units - Pay attention to units and include them in your answer when appropriate.

4. Making calculation errors - Double-check your arithmetic, especially when working with decimals or fractions.

5. Not checking if the answer makes sense - Consider whether your answer is reasonable in the context of the problem.

Tips for Solving Word Problems

1. Understand the problem - Identify what information is given and

The article now flows naturally, moving from one topic to the next while maintaining clarity and coherence. Each section builds on the previous one, guiding the reader through calculations and reasoning. The final conclusion effectively wraps up the key takeaways Easy to understand, harder to ignore. And it works..

Understanding the importance of careful reading and logical steps is essential in solving complex problems. By practicing these strategies, learners can enhance their problem-solving skills and confidence.

In a nutshell, attention to detail and systematic thinking are vital for success in these scenarios. Remembering these principles will help you tackle similar challenges with ease.

Conclusion: Mastering these concepts empowers you to approach problems with clarity and precision, ensuring accurate results every time.

Problem 7: Compound Interest

Problem: A savings account offers an annual interest rate of 3 % compounded quarterly. If you deposit $1,200 today, how much will be in the account after 5 years?

Solution:

1. Identify the variables:

   • Principal, (P = $1,200)
   • Annual nominal rate, (r = 0.03)
   • Number of compounding periods per year, (n = 4)
   • Time in years, (t = 5)

2. Compute the periodic rate: [ i = \frac{r}{n} = \frac{0.03}{4} = 0.0075 ]

3. Determine the total number of periods: [ N = n \times t = 4 \times 5 = 20 ]

4. Apply the compound‑interest formula: [ A = P(1+i)^N = 1200(1+0.0075)^{20} ]

5. Calculate: [ 1+0.0075 = 1.0075 ] [ 1.0075^{20} \approx 1.1616 ] [ A \approx 1200 \times 1.1616 \approx $1,393.92 ]

Answer: After five years, the account will hold approximately $1,393.92.

When to Use Different Problem‑Solving Strategies

Quick note before moving on.

Common Pitfalls in Word Problems

Practice Makes Perfect

Below are a few additional problems to sharpen your skills. Try solving them before reading the solutions.

1. Retail Discount – A jacket originally costs $80. It is on sale for 25 % off, and then a coupon provides an additional $10 off. What is the final price?
2. Speed and Time – A cyclist travels 30 km at 15 km/h and then 20 km at 10 km/h. What was the average speed for the entire trip?
3. Probability with Replacement – A bag contains 4 red, 3 blue, and 2 green marbles. Two marbles are drawn with replacement. What is the probability that both are blue?

Final Thoughts

Word problems are not just tests of arithmetic; they are opportunities to apply logic, translate real‑world situations into mathematical language, and verify that your solutions make sense. By:

1. Carefully reading the problem,
2. Translating words into equations or formulas,
3. Checking units and consistency,
4. Solving step by step, and
5. Reflecting on the answer’s plausibility,

you’ll build confidence and accuracy in tackling any quantitative challenge Simple, but easy to overlook. And it works..

Conclusion: Mastery of word‑problem strategies turns abstract numbers into meaningful answers. With practice, the steps become almost second nature, allowing you to approach new problems with clarity, precision, and a sense of assurance. Happy solving!

In addition to numerical precision, contextual awareness enhances problem-solving efficacy. Adapting strategies to unique scenarios demands flexibility, ensuring alignment with the problem’s specific demands. Such versatility underpins success across diverse domains.

Conclusion: Such awareness consolidates mathematical proficiency, fostering both competence and confidence in navigating complex challenges. Embracing these principles cultivates a mindset rooted in clarity and precision, ultimately empowering individuals to approach mathematics as a dynamic, collaborative endeavor Turns out it matters..