Gade 6 Math Word Problems with Step-by-Step Solutions

Welcome to our collection of Grade 6 math word problems with step-by-step solutions and clear explanations. These carefully designed problems help students practice critical thinking, improve problem-solving skills, and build a strong foundation in mathematics. Perfect for students, teachers, and parents looking for effective Grade 6 math resources.

Solutions to Word Problems


  1. Two numbers \( N \) and \( 16 \) have \( \text{LCM} = 48 \) and \( \text{GCF} = 8 \). Find \( N \).

    Solution


    The product of two integers is equal to the product of their LCM and GCF. Hence, \[ 16 \times N = 48 \times 8 \] \[ N = \dfrac{48 \times 8}{16} = 24 \]

  2. If the area of a circle is \( 81\pi \) square feet, find its circumference.

    Solution


    The area is given by \[ \pi r^2 = 81\pi \] \[ r^2 = 81 \quad \Rightarrow \quad r = 9 \] The circumference is \[ 2\pi r = 2\pi \times 9 = 18\pi \ \text{feet} \]

  3. Find the greatest common factor (GCF) of 24, 40 and 60.

    Solution


    We write the prime factorization: \[ 24 = 2^3 \times 3 \] \[ 40 = 2^3 \times 5 \] \[ 60 = 2^2 \times 3 \times 5 \] \[ \text{GCF} = 2^2 = 4 \]

  4. In a given school, there are 240 boys and 260 girls.
    a) What is the ratio of the number of girls to the number of boys?
    b) What is the ratio of the number of boys to the total number of pupils?

    Solution


    a) \[ 260 : 240 = 13 : 12 \] b) \[ 240 : (240 + 260) = 240 : 500 = 12 : 25 \]

  5. If Tim had lunch at \$50.50 and he gave a 20% tip, how much did he spend?

    Solution


    \[ \text{Tip} = 20\% \times 50.50 = \dfrac{20}{100} \times 50.50 = 10.10 \] \[ \text{Total} = 50.50 + 10.10 = \$60.60 \]

  6. Find \( k \) if \[ \dfrac{64}{k} = 4 \]

    Solution


    Since \[ \dfrac{64}{16} = 4 \] we have \[ k = 16 \]

  7. Little John had \$8.50. He spent \$1.25 on sweets and gave his two friends \$1.20 each. How much was left?

    Solution


    \[ 1.25 + 1.20 + 1.20 = 3.65 \] \[ 8.50 - 3.65 = 4.85 \]

  8. What is \( x \) if \[ x + 2y = 10, \quad y = 3 \]

    Solution


    \[ x + 2(3) = 10 \quad \Rightarrow \quad x + 6 = 10 \quad \Rightarrow \quad x = 4 \]

  9. A telephone company charges \$0.50 plus \$0.11 per minute. Write an expression for a call lasting \( N \) minutes.

    Solution


    \[ C = 0.50 + 0.11N \]

  10. A car gets 40 kilometers per gallon. How many gallons are needed for 180 kilometers?

    Solution


    \[ \dfrac{180}{40} = 4.5 \quad \Rightarrow \quad 4.5 \ \text{gallons} \]

  11. A machine fills 150 bottles every 8 minutes. How long to fill 675 bottles?

    Solution


    The number of groups of 150 bottles in 675 is \[ \dfrac{675}{150} = 4.5 \] Each group requires 8 minutes, so \[ 4.5 \times 8 = 36 \ \text{minutes} \] Hence, it takes 36 minutes.

  12. A car travels at 65 miles per hour. How far in 5 hours?

    Solution


    \[ 5 \times 65 = 325 \ \text{miles} \]

  13. A small square of side \( 2x \) is cut from a \( 20 \times 10 \) rectangle. Find the remaining area.

    Solution


    \[ A = 20 \times 10 = 200 \] \[ B = (2x)^2 = 4x^2 \] \[ \text{Remaining} = 200 - 4x^2 \]

  14. A rectangle \( A: 10 \times 5 \) is similar to rectangle \( B: 30 \times W_2 \). Find the area of \( B \).

    Solution


    \[ \dfrac{30}{10} = \dfrac{W_2}{5} \quad \Rightarrow \quad W_2 = 15 \] \[ \text{Area} = 30 \times 15 = 450 \ \text{cm}^2 \]

  15. A school has 10 equal classes. 70 students absent: 5 half-full, 3 three-quarters full, 2 with \( \tfrac{1}{8} \) absent. Find total enrolled.

    Solution


    \[ \dfrac{5}{2}x + \dfrac{3}{4}x + \dfrac{2}{8}x = 70 \] \[ \dfrac{28}{8}x = 70 \quad \Rightarrow \quad x = 20 \] \[ 10 \times 20 = 200 \ \text{students} \]

  16. A \( 4 \times 4 \) square is made of 16 unit squares. Count all squares.

    Solution


    There are squares of 4 different sizes:
    1. \(16\) squares of dimension \(1 \times 1\)
    2. \(9\) squares of dimension \(2 \times 2\)
    3. \(4\) squares of dimension \(3 \times 3\)
    4. \(1\) square of dimension \(4 \times 4\)
    In total: \[ 16 + 9 + 4 + 1 = 30 \]

  17. The perimeter of square \( A \) is 3 times that of square \( B \). Find ratio of their areas.

    Solution


    \[ 4x = 12y \quad \Rightarrow \quad x = 3y \] \[ \dfrac{x^2}{y^2} = \dfrac{(3y)^2}{y^2} = 9 \]

  18. John gave half of his stamps to Jim, who gave half to Carla. Carla kept 12 after giving \( \tfrac{1}{4} \) to Thomas. Find John’s original number.

    Solution


    \[ \dfrac{3}{4} \cdot \dfrac{1}{2} \cdot \dfrac{1}{2}x = 12 \] \[ \dfrac{3}{16}x = 12 \quad \Rightarrow \quad x = \dfrac{16}{3}\times12 = 64 \]

  19. Two balls: A takes 30 sec per rotation, B takes 20 sec. When will they meet again at start?

    Solution


    \[ \text{LCM}(30,20) = 60 \ \text{seconds} \]

  20. A 3-unit segment is divided into 9 parts. What fraction is 2 parts?

    Solution


    \[ 1 \ \text{part} = \dfrac{1}{3} \quad \Rightarrow \quad 2 \ \text{parts} = \dfrac{2}{3} \]

  21. Mary makes a box from \( 15 \times 10 \) cardboard cutting 3 cm squares. Find its volume.

    Solution


    \[ L = 15 - 6 = 9, \quad W = 10 - 6 = 4, \quad H = 3 \] \[ V = 9 \times 4 \times 3 = 108 \ \text{cm}^3 \]

  22. A car travels 75 km/h. How many meters in one minute?

    Solution


    \[ 75 \times \dfrac{1000}{60} = 1250 \ \text{meters per minute} \]

  23. Carla is 5. Jim is 13 years younger than Peter. One year ago, Peter’s age was twice the sum of Carla’s and Jim’s ages. Find their current ages.

    Solution


    \[ x - 1 = 2\left( (5-1) + (x-14) \right) \] \[ x - 1 = 2(x-10) \] \[ x = 19, \quad \text{Jim} = 6, \quad \text{Carla} = 5 \]

  24. Linda spent \( \tfrac{3}{4} \) of her savings on furniture, then half the rest (\$150) on a fridge. Find her original savings.

    Solution


    \[ \dfrac{1}{2}\left(\dfrac{1}{4}x\right) = 150 \] \[ \dfrac{x}{8} = 150 \quad \Rightarrow \quad x = 1200 \]

  25. Harry and Kate are 2500 m apart. Speeds: Harry 40 m/min, Kate 60 m/min, dog 120 m/min. How far will the dog run?

    Solution


    \[ t = \dfrac{2500}{40+60} = 25 \ \text{minutes} \] \[ d = 120 \times 25 = 3000 \ \text{meters} \]

References