Real-World Equations

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Real-World Equations · Grade 6 · Worksheet 1

1. Liam is planning a road trip and needs to calculate his fuel costs. His car gets 32 miles per gallon, and the total distance for his trip is 480 miles. If the current price of gasoline is $3.75 per gallon, how much money should Liam budget for gasoline for the entire trip? Answer: 56.25 Solution: First, find out how many gallons of gasoline Liam will need for the trip. The car's fuel efficiency is 32 miles per gallon, and the total distance is 480 miles.
   Full step-by-step solution

   First, find out how many gallons of gasoline Liam will need for the trip. The car's fuel efficiency is 32 miles per gallon, and the total distance is 480 miles. So, the number of gallons needed is the total distance divided by the miles per gallon. Gallons needed = 480 miles / 32 miles per gallon Calculate that: 480 / 32 = 15 So, Liam needs 15 gallons of gasoline for the trip. Next, calculate the total cost. The price of gasoline is $3.75 per gallon. Total cost = Gallons needed * Price per gallon Total cost = 15 * 3.75 Now, calculate 15 * 3.75. First, 15 * 3 = 45 Then, 15 * 0.75 = 11.25 Now, add them together: 45 + 11.25 = 56.25 So, the total cost for gasoline is $56.25. Therefore, Liam should budget $56.25 for gasoline for the entire trip.

2. Mere has 2048 points in a video game. She earns 576 more points. Write an equation using p for the total points. Answer: p = 2048 + 576 Solution: Identify the starting points: 2048. Identify the additional points earned: 576. To find the total, add the starting points and the additional points.
   Full step-by-step solution

   Step 1: Identify the starting points: 2048. Step 2: Identify the additional points earned: 576. Step 3: To find the total, add the starting points and the additional points. Step 4: Write the equation: p = 2048 + 576. Step 5: The equation representing the situation is p = 2048 + 576.

3. Kaia has 1375 points in a video game. Tane has 3 times as many points as Kaia. Write an equation to represent the number of points Tane has, using p for the number of points Tane has. Answer: p = 3 × 1375 Solution: Identify the known quantity: Kaia has 1375 points. Identify the relationship: Tane has 3 times as many points as Kaia. Choose a variable: Let p represent the number of points Tane has.
   Full step-by-step solution

   Step 1: Identify the known quantity: Kaia has 1375 points. Step 2: Identify the relationship: Tane has 3 times as many points as Kaia. Step 3: Choose a variable: Let p represent the number of points Tane has. Step 4: Write the equation: p = 3 × 1375 The equation is p = 3 × 1375.

4. Kaia is designing a rectangular mural on a coordinate grid. The four corners of the mural are at (9, 12), (33, 12), (33, 28), and (9, 28). She wants to paint a diagonal line from the bottom-left corner to the top-right corner of the mural. Write an equation to represent the length (L) of this diagonal line in units. Answer: L = sqrt(24^2 + 16^2) or L = sqrt(576 + 256) Solution: Identify the bottom-left corner as (9, 12) and the top-right corner as (33, 28). Find the horizontal distance: 33 - 9 = 24 units. Find the vertical distance: 28 - 12 = 16 units.
   Full step-by-step solution

   Step 1: Identify the bottom-left corner as (9, 12) and the top-right corner as (33, 28). Step 2: Find the horizontal distance: 33 - 9 = 24 units. Step 3: Find the vertical distance: 28 - 12 = 16 units. Step 4: The diagonal forms a right triangle with these distances as legs. Step 5: Use the Pythagorean theorem: L^2 = 24^2 + 16^2. Step 6: So L = sqrt(24^2 + 16^2) = sqrt(576 + 256) = sqrt(832). The equation is L = sqrt(24^2 + 16^2).

5. Mason has 1272 more points than Isabella in a video game. If Isabella has 2487 points, write an equation using p for Mason's points. Answer: p = 2487 + 1272 Solution: Identify the known values. Isabella has 2487 points. Mason has 1272 more points than Isabella.
   Full step-by-step solution

   Step 1: Identify the known values. Isabella has 2487 points. Mason has 1272 more points than Isabella. Step 2: Since Mason has more points, we add the difference to Isabella's points. Step 3: Let p represent Mason's points. The equation is p = 2487 + 1272. Step 4: The answer is p = 2487 + 1272.

6. Tane is saving money to buy a new bike. He already has $1275 and saves $85 each week. Write an equation to represent the total amount of money (m) Tane will have after w weeks. Answer: m = 1275 + 85w Solution: Identify the starting amount: $1275. Identify the weekly savings: $85 per week. Let w represent the number of weeks.
   Full step-by-step solution

   Step 1: Identify the starting amount: $1275. Step 2: Identify the weekly savings: $85 per week. Step 3: Let w represent the number of weeks. Step 4: The total saved after w weeks is 85w. Step 5: Add the starting amount: m = 1275 + 85w. The equation is m = 1275 + 85w.

7. Eva is baking cookies for a school bake sale. Each batch makes 24 cookies. Eva makes 2 batches. Write an equation to find the total number of cookies, c, Eva baked. Answer: 48 Solution: Each batch makes 24 cookies. Eva makes 2 batches. Total cookies = 24 × 2 = 48.
   Full step-by-step solution

   Step 1: Each batch makes 24 cookies. Step 2: Eva makes 2 batches. Step 3: Total cookies = 24 × 2 = 48. The equation is c = 24 × 2, so c = 48. The answer is 48 cookies.

8. Emma has 3 times as many stickers as Liam. Liam has s stickers. Write an equation for the number of stickers Emma has. Answer: 3s Solution: Identify the variable. Let s = the number of stickers Liam has. Emma has 3 times as many stickers as Liam.
   Full step-by-step solution

   Step 1: Identify the variable. Let s = the number of stickers Liam has. Step 2: Emma has 3 times as many stickers as Liam. 'Times' means multiplication. Step 3: So Emma's stickers = 3 × s = 3s. The equation is 3s.

9. Aroha is baking cookies for a school bake sale. Each batch makes 7 cookies. Aroha makes 5 batches. Write an equation to find the total number of cookies, c, Aroha baked. Answer: 35 Solution: Each batch makes 7 cookies. Aroha makes 5 batches. Total cookies = 7 × 5 = 35.
   Full step-by-step solution

   Step 1: Each batch makes 7 cookies. Step 2: Aroha makes 5 batches. Step 3: Total cookies = 7 × 5 = 35. The equation is c = 7 × 5, so c = 35. The answer is 35 cookies.