Which mathematical equation could represent the following verbal expression?"Half of an unknown number b is equal to the sum of a number that is 4 times greater than br and a number is 12 less than b

Answer 1

To translate the verbal expression into a mathematical equation, let's break it down step by step.

1. The phrase "Half of an unknown number b" can be represented as:
   \(\frac{b}{2}\).

2. The phrase "the sum of a number that is 4 times greater than b" can be interpreted as:
   \(4b\) (since "4 times greater than" can be misleading, it's commonly seen as just \(4b\)).

3. The phrase "a number that is 12 less than b" can be represented as:
   \(b - 12\).

Now we can combine these parts. The total sum of the two quantities mentioned (4 times greater than \(b\) and 12 less than \(b\)) is:
\[4b + (b - 12)\].

4. Setting these two expressions equal to each other, we get:
   \[ \frac{b}{2} = 4b + (b - 12). \]

Now, let's simplify the right side: \[ \frac{b}{2} = 4b + b - 12. \] This simplifies to: \[ \frac{b}{2} = 5b - 12. \]

Thus, the mathematical equation representing the verbal expression is: \[ \frac{b}{2} = 5b - 12. \]