Real-World Equations

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Real-World Equations · Grade 6 · Worksheet 3

1. Liam is designing a rectangular garden for his school project. The garden's length is 12.5 meters and its width is 8.4 meters. He wants to build a fence around the entire garden and then cover the entire area with sod. How many meters of fencing does he need for the perimeter, and how many square meters of sod does he need to cover the area? Answer: Perimeter: 41.8 meters, Area: 105 square meters Solution: Length of the garden = 12.5 meters Width of the garden = 8.4 meters The formula for the perimeter \( P \) of a rectangle is: P = 2 × (length + width) P = 2 × (12.5 + 8.4) 12.5 + 8.4 = 20.9 Now multiply by 2: P = 2 × 20.9 = 41.8 meters So, Liam needs 41.8 meters of fencing.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Identify the given dimensions** Length of the garden = 12.5 meters Width of the garden = 8.4 meters --- **Step 2: Find the perimeter** The formula for the perimeter \( P \) of a rectangle is: P = 2 × (length + width) Substitute the values: P = 2 × (12.5 + 8.4) First, add length and width: 12.5 + 8.4 = 20.9 Now multiply by 2: P = 2 × 20.9 = 41.8 meters So, Liam needs **41.8 meters** of fencing. --- **Step 3: Find the area** The formula for the area \( A \) of a rectangle is: A = length × width Substitute the values: A = 12.5 × 8.4 First, multiply ignoring decimals: 125 × 84 = ? 125 × 80 = 10,000 125 × 4 = 500 Total = 10,500 Now, since 12.5 has 1 decimal place and 8.4 has 1 decimal place, total decimal places = 2. So, 10,500 becomes 105.00 Thus, A = 105 square meters So, Liam needs **105 square meters** of sod. --- **Final Answer:** Perimeter: 41.8 meters, Area: 105 square meters

2. Liam is designing a rectangular garden for his school. The garden's length is 12.5 meters and its width is 8.4 meters. He needs to buy fencing to go around the entire garden and fertilizer to cover the garden's area. How many meters of fencing does he need for the perimeter, and how many square meters does he need fertilizer for? Answer: 41.8 meters and 105 square meters Solution: Length of garden = 12.5 meters Width of garden = 8.4 meters Perimeter of a rectangle = 2 × (length + width) Perimeter = 2 × (12.5 + 8.4) 12.5 + 8.4 = 20.9 meters Now multiply by 2: 2 × 20.9 = 41.8 meters So, fencing needed = 41.8 meters Area of a rectangle = length × width Area = 12.5 × 8.4…
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Identify what is given** Length of garden = 12.5 meters Width of garden = 8.4 meters --- **Step 2: Find the perimeter for fencing** Perimeter of a rectangle = 2 × (length + width) Perimeter = 2 × (12.5 + 8.4) First, add length and width: 12.5 + 8.4 = 20.9 meters Now multiply by 2: 2 × 20.9 = 41.8 meters So, fencing needed = **41.8 meters** --- **Step 3: Find the area for fertilizer** Area of a rectangle = length × width Area = 12.5 × 8.4 First, multiply 12.5 × 8.4: 12.5 × 8 = 100 12.5 × 0.4 = 5.0 Add them: 100 + 5.0 = 105.0 So, area = **105 square meters** --- **Step 4: Final answer** Fencing needed: 41.8 meters Fertilizer needed for: 105 square meters

3. A factory produces 2,400 units of a product every day. The units are packed into boxes that can hold 32 units each. After packing as many full boxes as possible, the remaining units are sent for quality testing. How many units are sent for quality testing? Answer: 0 Solution: The factory produces 2,400 units per day. Each box holds 32 units. We pack as many full boxes as possible, then the leftover units (if any) are sent for testing.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the problem** The factory produces 2,400 units per day. Each box holds 32 units. We pack as many full boxes as possible, then the leftover units (if any) are sent for testing. We need to find how many leftover units there are. --- **Step 2: Find how many full boxes can be packed** We divide the total units by the units per box: Number of full boxes = Total units ÷ Units per box = 2400 ÷ 32 --- **Step 3: Perform the division** Let's calculate 2400 ÷ 32: First, 32 × 75 = 2400 Check: 32 × 70 = 2240, plus 32 × 5 = 160, total 2240 + 160 = 2400. So 2400 ÷ 32 = 75 exactly. --- **Step 4: Interpret the result** Since 2400 ÷ 32 = 75 exactly, there are no leftover units. All units fit perfectly into full boxes. --- **Step 5: Conclusion** Remaining units after packing = Total units − (Full boxes × Units per box) = 2400 − (75 × 32) = 2400 − 2400 = 0 So, 0 units are sent for quality testing. --- **Final answer:** 0

4. Matiu collects trading cards. Matiu has 2 packs of cards. Each pack contains 6 cards. Write an equation to represent the total number of cards, t, that Matiu has. Answer: 12 Solution: Matiu has 2 packs. Each pack has 6 cards. Total cards = 2 × 6 = 12.
   Full step-by-step solution

   Step 1: Matiu has 2 packs. Step 2: Each pack has 6 cards. Step 3: Total cards = 2 × 6 = 12. The equation is t = 2 × 6, so t = 12. The answer is 12 cards.