Equation Word Problems

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Equation Word Problems · Grade 7 · Worksheet 2

1. Aroha is selling handmade scarves at a market. She has 135 meters of yarn. Each scarf requires 9 meters of yarn. She also needs to set aside 27 meters of yarn for a special order. After making as many scarves as possible with the remaining yarn, how many scarves can Aroha make? Answer: 12 Solution: Subtract the yarn for the special order from the total yarn: 135 - 27 = 108 meters remaining. Divide the remaining yarn by the yarn needed per scarf: 108 / 9 = 12 scarves. Aroha can make 12 scarves.
   Full step-by-step solution

   Step 1: Subtract the yarn for the special order from the total yarn: 135 - 27 = 108 meters remaining. Step 2: Divide the remaining yarn by the yarn needed per scarf: 108 / 9 = 12 scarves. Aroha can make 12 scarves.

2. A company's profit increased by 15% from Year 1 to Year 2, then decreased by 10% from Year 2 to Year 3. If the final profit in Year 3 was $124,200, what was the profit in Year 1 (in dollars)? Answer: 120000 Solution: Year 3 profit is 90% of Year 2 profit (since it decreased by 10%). Set up equation: Year 2 profit × 0.90 = 124,200 Solve for Year 2 profit: Year 2 profit = 124,200 ÷ 0.90 = 138,000 Now find Year 1 profit.
   Full step-by-step solution

   Step 1: Let's work backwards from Year 3 to find Year 2 profit. Year 3 profit is 90% of Year 2 profit (since it decreased by 10%). Step 2: Set up equation: Year 2 profit × 0.90 = 124,200 Step 3: Solve for Year 2 profit: Year 2 profit = 124,200 ÷ 0.90 = 138,000 Step 4: Now find Year 1 profit. Year 2 profit is 115% of Year 1 profit (since it increased by 15%). Step 5: Set up equation: Year 1 profit × 1.15 = 138,000 Step 6: Solve for Year 1 profit: Year 1 profit = 138,000 ÷ 1.15 = 120,000 Step 7: Verify: 120,000 × 1.15 = 138,000; 138,000 × 0.90 = 124,200 The answer is 120000.

3. Emma has three times as many books as Liam. Together, they have 96 books. How many books does Liam have? Answer: 24 Solution: Let x represent the number of books Liam has. Emma has three times as many books as Liam, so Emma has 3x books. Together they have 96 books, so the equation is x + 3x = 96.
   Full step-by-step solution

   Step 1: Let x represent the number of books Liam has. Step 2: Emma has three times as many books as Liam, so Emma has 3x books. Step 3: Together they have 96 books, so the equation is x + 3x = 96. Step 4: Combine like terms: 4x = 96. Step 5: Divide both sides by 4: x = 96 / 4 = 24. The answer is 24.

4. (-4)³ ÷ 8 + 5 × (3 - 7) = ? Answer: -28 Solution: Solve inside the parentheses: (3 - 7) = -4 Calculate the exponent: (-4)³ = -4 × -4 × -4 = -64 Perform division: -64 ÷ 8 = -8 Perform multiplication: 5 × (-4) = -20 Add the results: -8 + (-20) = -28 The final answer is -28.
   Full step-by-step solution

   Step 1: Solve inside the parentheses: (3 - 7) = -4 Step 2: Calculate the exponent: (-4)³ = -4 × -4 × -4 = -64 Step 3: Perform division: -64 ÷ 8 = -8 Step 4: Perform multiplication: 5 × (-4) = -20 Step 5: Add the results: -8 + (-20) = -28 The final answer is -28.

5. Mason is designing a rectangular garden on a coordinate grid. One corner of the garden is at (0, 0). The other three corners are at (0, 15), (22, 0), and (22, 15). A circular fountain with a radius of 3 meters is drawn centered at (11, 7). What is the area of the garden that is not covered by the fountain? (Use π = 3.14 and round your final answer to the nearest whole number.) Answer: 302 Solution: Find the dimensions of the rectangle. The width is the distance from (0,0) to (22,0) which is 22 meters. The height is the distance from (0,0) to (0,15) which is 15 meters.
   Full step-by-step solution

   Step 1: Find the dimensions of the rectangle. The width is the distance from (0,0) to (22,0) which is 22 meters. The height is the distance from (0,0) to (0,15) which is 15 meters. Step 2: Calculate the area of the rectangular garden: Area = length x width = 22 x 15 = 330 square meters. Step 3: Calculate the area of the circular fountain: Area = π x radius^2 = 3.14 x 3^2 = 3.14 x 9 = 28.26 square meters. Step 4: Subtract the fountain's area from the garden's area: 330 - 28.26 = 301.74 square meters. Step 5: Round to the nearest whole number: 302 square meters. The answer is 302.

6. Noah is saving money to buy a new laptop that costs $1,200. He has already saved $320. He plans to save an equal amount each month for the next 16 months. How much must he save each month? Answer: 55 Solution: Determine the amount Noah still needs to save: $1,200 - $320 = $880. Let x be the amount he saves each month. Over 16 months, he will save 16x dollars.
   Full step-by-step solution

   Step 1: Determine the amount Noah still needs to save: $1,200 - $320 = $880. Step 2: Let x be the amount he saves each month. Over 16 months, he will save 16x dollars. Step 3: Set up the equation: 16x = 880. Step 4: Solve for x: x = 880 / 16 = 55. Noah must save $55 each month.

7. Mere is saving money to buy a new laptop that costs $1,250. She already has $320 saved. She plans to save an equal amount of money each week for the next 15 weeks. How much money does Mere need to save each week to have exactly enough to buy the laptop? Answer: 62 Solution: Determine the total amount Mere still needs to save. She needs $1,250 and has $320. So, amount needed = 1250 - 320 = 930 dollars.
   Full step-by-step solution

   Step 1: Determine the total amount Mere still needs to save. She needs $1,250 and has $320. So, amount needed = 1250 - 320 = 930 dollars. Step 2: Let x be the amount Mere saves each week. She will save for 15 weeks, so the total saved is 15x. Step 3: Set up the equation: 15x = 930. Step 4: Solve for x by dividing both sides by 15: x = 930 / 15. Step 5: Calculate: 930 / 15 = 62. Step 6: Mere needs to save $62 each week. The answer is 62.

8. A triangular park is drawn on a coordinate plane with vertices at (0, 0), (12, 0), and (6, 9). A rectangular playground is built inside the park with corners at (3, 0), (9, 0), (9, 4.5), and (3, 4.5). What is the area of the park that remains as green space outside the playground? Answer: 27 Solution: Find the area of the triangular park. The base is from (0,0) to (12,0), so base = 12 units. The height is from the base to point (6,9), so height = 9 units.
   Full step-by-step solution

   Step 1: Find the area of the triangular park. The base is from (0,0) to (12,0), so base = 12 units. The height is from the base to point (6,9), so height = 9 units. Area of triangle = (1/2) × base × height = (1/2) × 12 × 9 = 54 square units. Step 2: Find the area of the rectangular playground. The length is from (3,0) to (9,0), so length = 6 units. The width is from the base to (9,4.5), so width = 4.5 units. Area of rectangle = length × width = 6 × 4.5 = 27 square units. Step 3: Subtract to find the remaining green space. Remaining area = triangle area - rectangle area = 54 - 27 = 27 square units. The answer is 27.