To solve for [tex]\( b \)[/tex] in the equation [tex]\( b \cdot c = 345\% \)[/tex] of [tex]\( c \)[/tex], let's follow the steps below:
1. Understand the problem: We are given that [tex]\( b \cdot c \)[/tex] represents [tex]\( 345\% \)[/tex] of a positive number [tex]\( c \)[/tex]. Our objective is to find the value of [tex]\( b \)[/tex].
2. Express the percentage in decimal form:
- [tex]\( 345\% \)[/tex] is equivalent to [tex]\( \frac{345}{100} \)[/tex] when converted into decimal form.
- Converting [tex]\( 345\% \)[/tex] to a decimal:
[tex]\[
\frac{345}{100} = 3.45
\][/tex]
3. Set up the equation: The equation given is:
[tex]\[
b \cdot c = 345\% \text{ of } c
\][/tex]
Replacing [tex]\( 345\% \)[/tex] with the decimal [tex]\( 3.45 \)[/tex], we get:
[tex]\[
b \cdot c = 3.45 \cdot c
\][/tex]
4. Isolate [tex]\( b \)[/tex]: To find the value of [tex]\( b \)[/tex], we need to isolate it on one side of the equation. Notice that [tex]\( c \)[/tex] appears on both sides of the equation:
[tex]\[
b \cdot c = 3.45 \cdot c
\][/tex]
We can divide both sides of the equation by [tex]\( c \)[/tex] (assuming [tex]\( c \ne 0 \)[/tex]):
[tex]\[
b = 3.45
\][/tex]
5. Conclude the solution: After simplifying, we find that the value of [tex]\( b \)[/tex] is:
[tex]\[
b = 3.45
\][/tex]
So the value of [tex]\( b \)[/tex] is [tex]\( 3.45 \)[/tex].
