Ruben is buying bricks for a project. He knows that 5 bricks weigh
pounds. He wants to know the weight of 24 bricks. What is the weight per brick?
pound(s) per brick At this rate, how much do 24 bricks weigh? pound(s)
The Correct Answer and Explanation is:
To solve this problem, let’s break it down step by step.
Step 1: Find the weight per brick
We are told that 5 bricks weigh a certain number of pounds (the number is missing in your question, so let’s use a placeholder and call it W pounds for now).
To find the weight of one brick, we divide the total weight by the number of bricks:Weight per brick=W5 pounds\text{Weight per brick} = \frac{W}{5} \text{ pounds}Weight per brick=5W pounds
Step 2: Find the weight of 24 bricks
Now that we have the weight of one brick, we multiply that by 24 to get the weight of 24 bricks:Weight of 24 bricks=24×W5=24W5 pounds\text{Weight of 24 bricks} = 24 \times \frac{W}{5} = \frac{24W}{5} \text{ pounds}Weight of 24 bricks=24×5W=524W pounds
Let’s assume a specific weight to continue the problem:
Suppose 5 bricks weigh 20 pounds.
Then:Weight per brick=205=4 pounds\text{Weight per brick} = \frac{20}{5} = 4 \text{ pounds}Weight per brick=520=4 poundsWeight of 24 bricks=24×4=96 pounds\text{Weight of 24 bricks} = 24 \times 4 = 96 \text{ pounds}Weight of 24 bricks=24×4=96 pounds
Final Answer:
- Weight per brick = 4 pounds
- Weight of 24 bricks = 96 pounds
Explanation
This is a proportional reasoning problem, where we are given a ratio (5 bricks weigh a certain amount) and asked to scale it up to a larger quantity (24 bricks). These types of problems are common in real-life situations involving materials, recipes, construction, or cost estimations.
First, we find the unit rate—in this case, the weight per single brick. To do this, we divide the total known weight by the number of bricks it corresponds to. Once we know the weight of one brick, it’s easy to find the weight of any number of bricks by multiplying that unit weight by the desired quantity.
Using the assumed data (5 bricks = 20 pounds), we calculated that each brick weighs 4 pounds. This makes sense because 4 pounds × 5 bricks = 20 pounds, confirming our unit rate is correct.
Then, to find the weight of 24 bricks, we multiply the single brick weight (4 pounds) by 24. The result is 96 pounds. Again, this checks out because if 5 bricks weigh 20 pounds, then 24 bricks, which is almost five times as many, should weigh close to five times more. Indeed, 20 × 4.8 = 96.
This logical approach ensures the answer makes sense both numerically and contextually.
