To solve the equation [tex]\(I = p \times r \times t\)[/tex] for [tex]\(t\)[/tex], follow these steps:
1. Understand the equation:
[tex]\[
I = p \times r \times t
\][/tex]
Here, [tex]\(I\)[/tex] is the interest, [tex]\(p\)[/tex] is the principal, [tex]\(r\)[/tex] is the rate, and [tex]\(t\)[/tex] is the time.
2. Isolate [tex]\(t\)[/tex]:
We need to solve for [tex]\(t\)[/tex], so we want [tex]\(t\)[/tex] by itself on one side of the equation.
3. Divide both sides by the product of [tex]\(p\)[/tex] and [tex]\(r\)[/tex]:
[tex]\[
\frac{I}{p \times r} = \frac{p \times r \times t}{p \times r}
\][/tex]
Simplifying the right-hand side, the [tex]\(p \times r\)[/tex] terms cancel out, leaving:
[tex]\[
\frac{I}{p \times r} = t
\][/tex]
Therefore, the equation solved for [tex]\(t\)[/tex] is:
[tex]\[
t = \frac{I}{p \times r}
\][/tex]
Among the given options:
1. [tex]\(I - p \times r = t \)[/tex] - This equation does not correctly isolate [tex]\(t\)[/tex].
2. [tex]\( \frac{I - p}{r} = t \)[/tex] - This equation does not correctly isolate [tex]\(t\)[/tex] either.
3. [tex]\( \frac{I}{p \times r} = t \)[/tex] - This is the correct equation solved for [tex]\(t\)[/tex].
4. [tex]\( I + p \times r = t \)[/tex] - This equation does not correctly isolate [tex]\(t\)[/tex].
Thus, the correct option is:
[tex]\[
\boxed{\frac{I}{p \times r} = t}
\][/tex]
