Question

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:
\[
\frac{b}{2} = 5b - 12.
\]