To find the value of [tex]\( r \)[/tex] when [tex]\( r \% \)[/tex] of 70 is 21, follow these steps:
1. Understand the relationship: [tex]\( r \% \)[/tex] of 70 implies that [tex]\( r \)[/tex] percent of 70 is equal to 21. Mathematically, this can be written as:
[tex]\[
\frac{r}{100} \times 70 = 21
\][/tex]
2. Convert the percentage to a decimal: Recall that [tex]\( r \% \)[/tex] is the same as [tex]\(\frac{r}{100} \)[/tex].
3. Write the equation: Substitute the known values into the equation:
[tex]\[
\frac{r}{100} \times 70 = 21
\][/tex]
4. Solve for [tex]\( r \)[/tex]:
[tex]\[
\frac{r \times 70}{100} = 21
\][/tex]
5. Isolate [tex]\( r \)[/tex] by multiplying both sides of the equation by 100 to eliminate the denominator:
[tex]\[
r \times 70 = 21 \times 100
\][/tex]
[tex]\[
r \times 70 = 2100
\][/tex]
6. Finally, divide both sides by 70 to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \frac{2100}{70}
\][/tex]
[tex]\[
r = 30
\][/tex]
Thus, the value of [tex]\( r \)[/tex] is [tex]\( 30 \)[/tex].
