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One Variable Equations

Grade 6 · Algebra · Worksheet 2

  1. x + 1570 = 2845. Solve for x. Answer: ______________
  2. At the school bake sale, Hana sold 11 boxes of cookies. Each box contains the same number of cookies. In total, Hana sold 132 cookies. How many cookies were in each box? Answer: ______________
  3. Noah is designing a community garden for his neighborhood. The rectangular garden will have a length that is 8 meters more than twice its width. If the total perimeter of the garden needs to be 76 meters to fit within the available space, what is the width of the garden in meters? Answer: ______________
  4. x + 1350 = 2800. Solve for x. Answer: ______________
  5. 3(x + 5) - 2(x - 3) = 42 Answer: ______________
  6. Liam is saving money to buy a new video game that costs $65. He already has $28 saved from his allowance. For his birthday, his grandmother gives him some money, and after adding this to his savings, he has exactly enough to buy the game. Which equation could be used to find m, the amount of money his grandmother gave him? Answer: ______________
  7. Sophia is looking at a scale drawing of a rectangular park. The length of the park in the drawing is 12 cm, and the actual length of the park is 2400 meters. If the width of the park in the drawing is 7 cm, what is the actual width of the park in meters? Answer: ______________
  8. Zoe planted a row of 8 flowers in the garden. Then Zoe planted some more flowers to make a total of 11 flowers in the row. How many additional flowers did Zoe plant? Answer: ______________
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Answer Key & Explanations

One Variable Equations · Grade 6 · Worksheet 2

  1. x + 1570 = 2845. Solve for x. Answer: 1275 Solution: The equation is x + 1570 = 2845. To isolate x, subtract 1570 from both sides of the equation. x + 1570 - 1570 = 2845 - 1570 Simplify: x = 1275 Check: 1275 + 1570 = 2845.
    Full step-by-step solution

    Step 1: The equation is x + 1570 = 2845. Step 2: To isolate x, subtract 1570 from both sides of the equation. Step 3: x + 1570 - 1570 = 2845 - 1570 Step 4: Simplify: x = 1275 Step 5: Check: 1275 + 1570 = 2845. ✓ The answer is 1275.

  2. At the school bake sale, Hana sold 11 boxes of cookies. Each box contains the same number of cookies. In total, Hana sold 132 cookies. How many cookies were in each box? Answer: 12 Solution: Let x represent the number of cookies per box. Write the equation: 11 × x = 132. Divide both sides by 11: x = 132 ÷ 11.
    Full step-by-step solution

    Step 1: Let x represent the number of cookies per box. Step 2: Write the equation: 11 × x = 132. Step 3: Divide both sides by 11: x = 132 ÷ 11. Step 4: Calculate: x = 12. Each box contained 12 cookies.

  3. Noah is designing a community garden for his neighborhood. The rectangular garden will have a length that is 8 meters more than twice its width. If the total perimeter of the garden needs to be 76 meters to fit within the available space, what is the width of the garden in meters? Answer: 10 Solution: Let w represent the width of the garden in meters. The length is 8 meters more than twice the width, so length = 2w + 8. The formula for perimeter of a rectangle is P = 2(length + width).
    Full step-by-step solution

    Step 1: Let w represent the width of the garden in meters. Step 2: The length is 8 meters more than twice the width, so length = 2w + 8. Step 3: The formula for perimeter of a rectangle is P = 2(length + width). Step 4: Substitute the known values: 76 = 2((2w + 8) + w) Step 5: Simplify inside the parentheses: 76 = 2(3w + 8) Step 6: Distribute the 2: 76 = 6w + 16 Step 7: Subtract 16 from both sides: 76 - 16 = 6w, so 60 = 6w Step 8: Divide both sides by 6: w = 60 ÷ 6 = 10 Step 9: The width of the garden is 10 meters.

  4. x + 1350 = 2800. Solve for x. Answer: 1450 Solution: The equation is x + 1350 = 2800. To isolate x, subtract 1350 from both sides of the equation: x + 1350 - 1350 = 2800 - 1350. Simplify: x = 1450.
    Full step-by-step solution

    Step 1: The equation is x + 1350 = 2800. Step 2: To isolate x, subtract 1350 from both sides of the equation: x + 1350 - 1350 = 2800 - 1350. Step 3: Simplify: x = 1450. Step 4: Check: 1450 + 1350 = 2800, which is correct. The answer is 1450.

  5. 3(x + 5) - 2(x - 3) = 42 Answer: 21 Solution: Distribute the 3: 3(x + 5) = 3x + 15 Distribute the -2: -2(x - 3) = -2x + 6 Rewrite the equation: 3x + 15 - 2x + 6 = 42 Combine like terms: (3x - 2x) + (15 + 6) = 42 Simplify: x + 21 = 42 Subtract 21 from both sides: x = 42 - 21 Calculate: x = 21 The answer is 21.
    Full step-by-step solution

    Step 1: Distribute the 3: 3(x + 5) = 3x + 15 Step 2: Distribute the -2: -2(x - 3) = -2x + 6 Step 3: Rewrite the equation: 3x + 15 - 2x + 6 = 42 Step 4: Combine like terms: (3x - 2x) + (15 + 6) = 42 Step 5: Simplify: x + 21 = 42 Step 6: Subtract 21 from both sides: x = 42 - 21 Step 7: Calculate: x = 21 The answer is 21.

  6. Liam is saving money to buy a new video game that costs $65. He already has $28 saved from his allowance. For his birthday, his grandmother gives him some money, and after adding this to his savings, he has exactly enough to buy the game. Which equation could be used to find m, the amount of money his grandmother gave him? Answer: 28 + m = 65 Solution: - Cost of the video game = $65 - Liam already has $28 saved. - His grandmother gives him some money, which we call m. - After adding the grandmother's money to his savings, he has exactly enough to buy the game.
    Full step-by-step solution

    Let's break this problem down step by step. --- **Step 1: Understand what we know** - Cost of the video game = $65 - Liam already has $28 saved. - His grandmother gives him some money, which we call **m**. - After adding the grandmother's money to his savings, he has exactly enough to buy the game. --- **Step 2: Set up the relationship** Liam's total money after the gift = Money he already had + Money from grandmother = 28 + m We know this total equals the cost of the game: 28 + m = 65 --- **Step 3: Verify the equation** The equation 28 + m = 65 directly represents the situation: - 28 is the initial savings - m is the unknown gift amount - 65 is the total needed No other operations are needed — no subtraction yet, because the problem only asks for the equation to find m, not to solve it. --- **Step 4: Conclusion** The correct equation is: 28 + m = 65 --- **Final answer:** 28 + m = 65

  7. Sophia is looking at a scale drawing of a rectangular park. The length of the park in the drawing is 12 cm, and the actual length of the park is 2400 meters. If the width of the park in the drawing is 7 cm, what is the actual width of the park in meters? Answer: 1400 Solution: Find the scale factor from the drawing to the actual park using the given length. Scale factor = actual length / drawing length = 2400 meters / 12 cm = 200 meters per cm.
    Full step-by-step solution

    Step 1: Find the scale factor from the drawing to the actual park using the given length. Scale factor = actual length / drawing length = 2400 meters / 12 cm = 200 meters per cm. Step 2: Apply this scale factor to the drawing width to find the actual width. Actual width = drawing width * scale factor = 7 cm * 200 meters/cm = 1400 meters. The actual width of the park is 1400 meters.

  8. Zoe planted a row of 8 flowers in the garden. Then Zoe planted some more flowers to make a total of 11 flowers in the row. How many additional flowers did Zoe plant? Answer: 3 Solution: Let x represent the additional flowers planted. Write the equation: 8 + x = 11. Subtract 8 from both sides: x = 11 - 8.
    Full step-by-step solution

    Step 1: Let x represent the additional flowers planted. Step 2: Write the equation: 8 + x = 11. Step 3: Subtract 8 from both sides: x = 11 - 8. Step 4: Calculate: x = 3. Zoe planted 3 more flowers.