Equation Word Problems

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Equation Word Problems · Grade 7 · Worksheet 1

1. Emma is planning a road trip from her home in Chicago to visit her grandparents in Denver, a distance of 1,008 miles. Her car can travel 32 miles per gallon of gas, and gas costs $3.50 per gallon. If she also needs to pay $45 for tolls during the trip, how much will Emma spend in total on gas and tolls for the entire round trip? Answer: $265.50 Solution: One way distance = 1,008 miles Round trip distance = 1,008 × 2 = 2,016 miles Gas mileage = 32 miles per gallon Gallons needed = 2,016 ÷ 32 = 63 gallons Gas price = $3.50 per gallon Gas cost = 63 × $3.50 = $220.50 Tolls = $45 Total cost = $220.50 + $45 = $265.50 The answer is $265.50.
   Full step-by-step solution

   Step 1: Calculate the total distance for the round trip One way distance = 1,008 miles Round trip distance = 1,008 × 2 = 2,016 miles Step 2: Calculate how many gallons of gas are needed Gas mileage = 32 miles per gallon Gallons needed = 2,016 ÷ 32 = 63 gallons Step 3: Calculate the cost of gas Gas price = $3.50 per gallon Gas cost = 63 × $3.50 = $220.50 Step 4: Add toll costs Tolls = $45 Total cost = $220.50 + $45 = $265.50 The answer is $265.50.

2. 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.

3. Liam is designing a rectangular garden with a length-to-width ratio of 5:3. He wants the garden to have an area of 1,215 square meters. What are the actual dimensions of Liam's garden? Answer: 45 meters by 27 meters Solution: The length-to-width ratio is 5:3. Let the length be \( 5x \) meters and the width be \( 3x \) meters, where \( x \) is a positive number.
   Full step-by-step solution

   Let's solve this step by step. --- **Step 1: Understand the ratio** The length-to-width ratio is 5:3. Let the length be \( 5x \) meters and the width be \( 3x \) meters, where \( x \) is a positive number. --- **Step 2: Write the area equation** Area of rectangle = length × width \[ (5x) \times (3x) = 1215 \] --- **Step 3: Simplify and solve for \( x \)** \[ 15x^2 = 1215 \] Divide both sides by 15: \[ x^2 = 1215 / 15 \] \[ 1215 / 15 = 81 \] So: \[ x^2 = 81 \] \[ x = \sqrt{81} = 9 \] (We take the positive root since dimensions are positive.) --- **Step 4: Find actual dimensions** Length = \( 5x = 5 \times 9 = 45 \) meters Width = \( 3x = 3 \times 9 = 27 \) meters --- **Step 5: Check** Area = \( 45 \times 27 = 1215 \) square meters ✓ Ratio = \( 45 : 27 = 5 : 3 \) ✓ --- **Final answer:** Length = 45 meters, Width = 27 meters

4. Emma is designing a rectangular garden on a coordinate grid. She plots the four corners of the garden at points A(0, 0), B(0, y), C(25, y), and D(25, 0). She then draws a straight path from corner A to corner C, dividing the garden into two triangular sections. If the area of the entire garden is 375 square meters, what is the value of y, the width of the garden? Answer: 15 Solution: Identify the length and width from the coordinates. The length is the horizontal distance from (0,0) to (25,0), which is 25 meters. The width is the vertical distance from (0,0) to (0,y), which is y meters.
   Full step-by-step solution

   Step 1: Identify the length and width from the coordinates. The length is the horizontal distance from (0,0) to (25,0), which is 25 meters. The width is the vertical distance from (0,0) to (0,y), which is y meters. Step 2: Write the area formula for a rectangle: Area = length × width. Step 3: Substitute the known area and length: 375 = 25 × y. Step 4: Solve for y by dividing both sides by 25: y = 375 ÷ 25. Step 5: Calculate: 375 ÷ 25 = 15. The answer is 15 meters.

5. Hana is drawing a rectangular garden on a coordinate grid. The garden has vertices at (0, 0), (24, 0), (24, 16), and (0, 16). She plans to build a square flower bed in one corner of the garden, with vertices at (0, 0), (8, 0), (8, 8), and (0, 8). The rest of the garden will be planted with grass. What is the area of the grassy part of the garden? Answer: 320 Solution: Find the area of the whole rectangular garden. The garden has length 24 units and width 16 units. Area = length × width = 24 × 16 = 384 square units.
   Full step-by-step solution

   Step 1: Find the area of the whole rectangular garden. The garden has length 24 units and width 16 units. Area = length × width = 24 × 16 = 384 square units. Step 2: Find the area of the square flower bed. The square has side length 8 units. Area = side × side = 8 × 8 = 64 square units. Step 3: Subtract the flower bed area from the garden area to find the grassy area. Grassy area = 384 − 64 = 320 square units. The answer is 320.

6. Emma is saving money to buy a new laptop that costs $1,200. She already has $320 saved. She plans to save an equal amount each month for the next 16 months. How much must she save each month to reach her goal? Answer: 55 Solution: Let x be the amount Emma saves each month. The total amount saved after 16 months is 320 + 16x. Set up the equation: 320 + 16x = 1200.
   Full step-by-step solution

   Step 1: Let x be the amount Emma saves each month. Step 2: The total amount saved after 16 months is 320 + 16x. Step 3: Set up the equation: 320 + 16x = 1200. Step 4: Subtract 320 from both sides: 16x = 880. Step 5: Divide both sides by 16: x = 55. Emma must save $55 each month.

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.