Pregunta
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Concrete building blocks weigh 28 pounds each. Using b for the number of concrete blocks and w for the weight, write two equations that relate the two variables. One equation should begin with \( w= \) and the other should begin with \( b= \).

Ask by Warren Christensen. in the United States
Jan 23,2025

Solución de tutoría real

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\( w = 28b \) and \( b = \frac{w}{28} \).

Solución

Given that each concrete block weighs 28 pounds, and letting \( b \) represent the number of blocks and \( w \) represent the total weight, the relationships between these variables can be expressed with the following two equations: 1. **Equation starting with \( w = \):** \[ w = 28b \] *This equation states that the total weight \( w \) is equal to 28 pounds multiplied by the number of blocks \( b \).* 2. **Equation starting with \( b = \):** \[ b = \frac{w}{28} \] *This equation shows that the number of blocks \( b \) is equal to the total weight \( w \) divided by 28 pounds.* These equations allow you to calculate either the total weight based on the number of blocks or the number of blocks based on the total weight. **Summary of the Equations:** \[ w = 28b \] \[ b = \frac{w}{28} \]

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Bonus Knowledge

A great way to relate the weight of the concrete blocks to their quantity is by considering the total weight equation. Since each block weighs 28 pounds, you can express the weight in relation to the number of blocks as \( w = 28b \). This formula tells you that the total weight is equal to 28 times the number of blocks. On the other hand, if you're looking to express the count of blocks in relation to the total weight, you can rearrange the equation to get \( b = \frac{w}{28} \). This indicates that the number of blocks can be found by dividing the total weight by the weight of each block. Let the block party begin!

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