Equation Word Problems

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Equation Word Problems · Grade 7 · Worksheet 3

1. A school is planning a field trip for 240 students. They need to rent buses that can each hold 36 students and vans that can each hold 8 students. The school wants to use exactly 10 vehicles in total for the trip. How many buses and how many vans should they rent to transport all students? Answer: 4 buses and 6 vans Solution: This type of problem involves solving a system of equations with two variables.
   Full step-by-step solution

   This type of problem involves solving a system of equations with two variables. You can represent the unknowns with variables, set up equations based on the constraints, and then use substitution or elimination to find the values that satisfy both conditions simultaneously.

2. Mason is saving money to buy a new bicycle that costs $252. He already has $67 saved. He plans to mow lawns in his neighborhood for $17 per lawn. How many lawns does Mason need to mow to have exactly enough money to buy the bicycle? Answer: 11 Solution: Let x represent the number of lawns Mason needs to mow. The total money from mowing is 17x dollars. He already has $67, so total money = 67 + 17x.
   Full step-by-step solution

   Step 1: Let x represent the number of lawns Mason needs to mow. Step 2: The total money from mowing is 17x dollars. He already has $67, so total money = 67 + 17x. Step 3: Set up the equation: 67 + 17x = 252. Step 4: Subtract 67 from both sides: 17x = 252 - 67 = 185. Step 5: Divide both sides by 17: x = 185 / 17 = 11. Step 6: Mason needs to mow 11 lawns. The answer is 11.

3. Emma is saving money to buy a new laptop that costs $1,215. She has already saved $351. She plans to save an equal amount each week for the next 9 weeks. How much money does Emma need to save each week to reach her goal? Answer: 96 Solution: Determine the total amount Emma still needs to save. Total cost of laptop: $1,215 Amount already saved: $351 Amount still needed: 1,215 - 351 = 864 Write an equation to represent the weekly savings.
   Full step-by-step solution

   Step 1: Determine the total amount Emma still needs to save. Total cost of laptop: $1,215 Amount already saved: $351 Amount still needed: 1,215 - 351 = 864 Step 2: Write an equation to represent the weekly savings. Let x = amount saved each week. 9 weeks of saving x dollars each week will give her 9x dollars. This must equal the amount still needed: 9x = 864 Step 3: Solve for x. Divide both sides by 9: x = 864 ÷ 9 = 96 Step 4: State the answer. Emma needs to save $96 each week.

4. Emma is planning a road trip from Chicago to Denver, a distance of 1,008 miles. Her car can travel 32 miles per gallon of gasoline, and gasoline costs $3.50 per gallon. If she wants to budget for the entire trip's fuel cost, how much money should Emma set aside for gasoline? Answer: 110.25 Solution: Calculate the total gallons of gasoline needed for the trip. Distance = 1,008 miles Miles per gallon = 32 Gallons needed = 1,008 ÷ 32 = 31.5 gallons Calculate the total cost for the gasoline.
   Full step-by-step solution

   Step 1: Calculate the total gallons of gasoline needed for the trip. Distance = 1,008 miles Miles per gallon = 32 Gallons needed = 1,008 ÷ 32 = 31.5 gallons Step 2: Calculate the total cost for the gasoline. Cost per gallon = $3.50 Total cost = 31.5 × 3.50 31.5 × 3.50 = 31.5 × 3 + 31.5 × 0.50 = 94.5 + 15.75 = 110.25 Emma should set aside $110.25 for gasoline.

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. If he builds a fence around the entire garden, how many meters of fencing will he need? Answer: 64 Solution: The ratio of length to width is 5:3.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Define variables for length and width** The ratio of length to width is 5:3. Let length = 5x Let width = 3x --- **Step 2: Write the area equation** Area = length × width 240 = (5x) × (3x) 240 = 15x² --- **Step 3: Solve for x** x² = 240 / 15 x² = 16 x = 4 (since length and width must be positive) --- **Step 4: Find length and width** Length = 5x = 5 × 4 = 20 meters Width = 3x = 3 × 4 = 12 meters --- **Step 5: Find the perimeter (fencing needed)** Perimeter = 2 × (length + width) Perimeter = 2 × (20 + 12) Perimeter = 2 × 32 Perimeter = 64 meters --- **Final answer:** 64 meters of fencing.

6. Liam has 15 more trading cards than Olivia. Together, they have 137 cards. How many cards does Olivia have? Answer: 61 Solution: Let x = number of cards Olivia has. Liam has 15 more than Olivia, so Liam has x + 15 cards. Together they have 137 cards, so the equation is: x + (x + 15) = 137.
   Full step-by-step solution

   Step 1: Let x = number of cards Olivia has. Step 2: Liam has 15 more than Olivia, so Liam has x + 15 cards. Step 3: Together they have 137 cards, so the equation is: x + (x + 15) = 137. Step 4: Combine like terms: 2x + 15 = 137. Step 5: Subtract 15 from both sides: 2x = 122. Step 6: Divide both sides by 2: x = 61. Olivia has 61 cards.

7. Charlotte is saving money to buy a new laptop that costs $1,200. She already has $320 saved and plans to save an equal amount each week for 16 weeks. How much money must Charlotte save each week to reach her goal? Answer: 55 Solution: Let x be the amount Charlotte saves each week. She saves for 16 weeks, so total saved is 16x. She already has $320, so total money after 16 weeks is 16x + 320.
   Full step-by-step solution

   Step 1: Let x be the amount Charlotte saves each week. Step 2: She saves for 16 weeks, so total saved is 16x. Step 3: She already has $320, so total money after 16 weeks is 16x + 320. Step 4: This must equal the laptop cost: 16x + 320 = 1200. Step 5: Subtract 320 from both sides: 16x = 880. Step 6: Divide both sides by 16: x = 55. Charlotte must save $55 each week.

8. Emma is planning a road trip from Chicago to Denver, a distance of 1,012 miles. Her car can travel 23 miles per gallon of gasoline, and gasoline costs $3.75 per gallon. If she wants to budget for the entire trip's fuel cost, how much money should Emma plan to spend on gasoline? Answer: 165 Solution: Calculate the total gallons of gasoline needed for the trip. Distance = 1,012 miles Miles per gallon = 23 Gallons needed = 1,012 ÷ 23 1,012 ÷ 23 = 44 So Emma needs 44 gallons of gasoline.
   Full step-by-step solution

   Step 1: Calculate the total gallons of gasoline needed for the trip. Distance = 1,012 miles Miles per gallon = 23 Gallons needed = 1,012 ÷ 23 1,012 ÷ 23 = 44 So Emma needs 44 gallons of gasoline. Step 2: Calculate the total cost of the gasoline. Cost per gallon = $3.75 Total cost = 44 × 3.75 44 × 3.75 = 165 Therefore, Emma should plan to spend $165 on gasoline for her trip.