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Equation Word Problems

Grade 7 · Algebra · Worksheet 2

  1. Mason is drawing a rectangular garden on a coordinate grid. One corner of the garden is at (2, 3). The garden has a length of 9 units horizontally and a width of 7 units vertically. What is the area of the garden in square units?
    Answer: ______________
  2. Olivia is saving money to buy a new bicycle that costs $255. She already has $75 saved. She plans to save $15 each week from her allowance. How many weeks will it take Olivia to save enough money to buy the bicycle? Answer: ______________
  3. A rectangular prism is drawn on a coordinate plane with vertices at (0, 0, 0), (8, 0, 0), (8, 5, 0), (0, 5, 0), (0, 0, 6), (8, 0, 6), (8, 5, 6), and (0, 5, 6). A smaller cube with side length 2 units is removed from one corner, positioned with its vertices at (0, 0, 0), (2, 0, 0), (2, 2, 0), (0, 2, 0), (0, 0, 2), (2, 0, 2), (2, 2, 2), and (0, 2, 2). What is the volume of the remaining solid?
    Answer: ______________
  4. Tane is saving money to buy a new laptop that costs $1,200. He already has $320 saved. He plans to mow lawns over the summer to earn the rest of the money. Each lawn he mows pays him $25. Write an equation to represent the situation and solve it to find how many lawns Tane needs to mow to have exactly enough money for the laptop. Answer: ______________
  5. Liam is designing a rectangular garden with a length-to-width ratio of 5:3. He wants the garden to have an area of exactly 240 square meters. What should be the dimensions of Liam's garden in meters? Answer: ______________
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Answer Key & Explanations

Equation Word Problems · Grade 7 · Worksheet 2

  1. Mason is drawing a rectangular garden on a coordinate grid. One corner of the garden is at (2, 3). The garden has a length of 9 units horizontally and a width of 7 units vertically. What is the area of the garden in square units? Answer: 63 Solution: Identify the dimensions. The length is 9 units and the width is 7 units. Recall the formula for the area of a rectangle: Area = length x width.
    Full step-by-step solution

    Step 1: Identify the dimensions. The length is 9 units and the width is 7 units. Step 2: Recall the formula for the area of a rectangle: Area = length x width. Step 3: Substitute the given values: Area = 9 x 7 = 63 square units. The answer is 63.

  2. Olivia is saving money to buy a new bicycle that costs $255. She already has $75 saved. She plans to save $15 each week from her allowance. How many weeks will it take Olivia to save enough money to buy the bicycle? Answer: 12 Solution: Determine the amount Olivia still needs to save. Total cost = $255, amount saved = $75. Amount needed = 255 - 75 = $180.
    Full step-by-step solution

    Step 1: Determine the amount Olivia still needs to save. Total cost = $255, amount saved = $75. Amount needed = 255 - 75 = $180. Step 2: Let x represent the number of weeks Olivia needs to save. She saves $15 each week, so the equation is: 15x = 180. Step 3: Solve for x by dividing both sides by 15: x = 180 / 15 = 12. Step 4: It will take Olivia 12 weeks to save enough money to buy the bicycle. Final answer: 12.

  3. A rectangular prism is drawn on a coordinate plane with vertices at (0, 0, 0), (8, 0, 0), (8, 5, 0), (0, 5, 0), (0, 0, 6), (8, 0, 6), (8, 5, 6), and (0, 5, 6). A smaller cube with side length 2 units is removed from one corner, positioned with its vertices at (0, 0, 0), (2, 0, 0), (2, 2, 0), (0, 2, 0), (0, 0, 2), (2, 0, 2), (2, 2, 2), and (0, 2, 2). What is the volume of the remaining solid? Answer: 232 Solution: Length = 8 units, Width = 5 units, Height = 6 units Volume of prism = length × width × height = 8 × 5 × 6 = 240 cubic units Side length = 2 units Volume of cube = side × side × side = 2 × 2 × 2 = 8 cubic units Subtract the cube's volume from the prism's volume Remaining volume = 240 - 8 = 232…
    Full step-by-step solution

    Step 1: Calculate the volume of the rectangular prism Length = 8 units, Width = 5 units, Height = 6 units Volume of prism = length × width × height = 8 × 5 × 6 = 240 cubic units Step 2: Calculate the volume of the cube that was removed Side length = 2 units Volume of cube = side × side × side = 2 × 2 × 2 = 8 cubic units Step 3: Subtract the cube's volume from the prism's volume Remaining volume = 240 - 8 = 232 cubic units The answer is 232.

  4. Tane is saving money to buy a new laptop that costs $1,200. He already has $320 saved. He plans to mow lawns over the summer to earn the rest of the money. Each lawn he mows pays him $25. Write an equation to represent the situation and solve it to find how many lawns Tane needs to mow to have exactly enough money for the laptop. Answer: 35.2 Solution: Let x be the number of lawns Tane needs to mow. The total money from mowing lawns is 25x dollars. He already has $320, so his total savings will be 320 + 25x.
    Full step-by-step solution

    Step 1: Let x be the number of lawns Tane needs to mow. Step 2: The total money from mowing lawns is 25x dollars. Step 3: He already has $320, so his total savings will be 320 + 25x. Step 4: Set this equal to the cost of the laptop: 320 + 25x = 1200. Step 5: Subtract 320 from both sides: 25x = 1200 - 320 = 880. Step 6: Divide both sides by 25: x = 880 / 25 = 35.2. Step 7: Since Tane cannot mow a fraction of a lawn, he would need to mow 36 lawns to have at least enough money. However, the equation gives exactly 35.2 lawns for the exact amount, so the answer to the equation is 35.2. The answer is 35.2.

  5. Liam is designing a rectangular garden with a length-to-width ratio of 5:3. He wants the garden to have an area of exactly 240 square meters. What should be the dimensions of Liam's garden in meters? Answer: 20 meters by 12 meters Solution: The ratio of length to width is 5:3.
    Full step-by-step solution

    Let's solve this step-by-step. --- **Step 1: Define variables for length and width** The ratio of length to width is 5:3. Let length = 5x meters Let width = 3x meters --- **Step 2: Write the equation for area** Area of a rectangle = length × width Area = (5x) × (3x) = 15x² We are told the area is 240 square meters, so: 15x² = 240 --- **Step 3: Solve for x** Divide both sides by 15: x² = 240 / 15 x² = 16 Take the positive square root (since dimensions are positive): x = 4 --- **Step 4: Find length and width** Length = 5x = 5 × 4 = 20 meters Width = 3x = 3 × 4 = 12 meters --- **Step 5: Verify** Area = 20 × 12 = 240 square meters ✓ Ratio = 20 : 12 = 5 : 3 ✓ --- **Final answer:** Length = 20 meters, Width = 12 meters