Alright, let's break down each step to solve these problems individually.
### (i) Finding the number whose 14% is 28:
1. Identify the given values:
- We know that 14% of some number is 28.
2. Set up the equation:
- Let [tex]\( x \)[/tex] be the unknown number.
- We can express this relationship as: [tex]\( 0.14x = 28 \)[/tex].
3. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], divide both sides of the equation by 0.14.
[tex]\[
x = \frac{28}{0.14}
\][/tex]
After performing the division:
[tex]\[
x \approx 200
\][/tex]
### (ii) Finding the number whose [tex]\( 16 \frac{2}{3} \% \)[/tex] is 3:
1. Identify the given values:
- We know that [tex]\( 16 \frac{2}{3} \% = \frac{50}{3} \% \)[/tex] of some number is 3.
2. Convert the percentage to a decimal:
- To work with it more easily, convert [tex]\( \frac{50}{3} \% \)[/tex] to a decimal by dividing by 100:
[tex]\[
\frac{50}{3} \% = \frac{50}{300} = \frac{1}{6}
\][/tex]
3. Set up the equation:
- Let [tex]\( y \)[/tex] be the unknown number.
- We can express this relationship as: [tex]\( \left(\frac{1}{6}\right) y = 3 \)[/tex].
4. Solve for [tex]\( y \)[/tex]:
- To isolate [tex]\( y \)[/tex], multiply both sides of the equation by 6.
[tex]\[
y = 3 \times 6
\][/tex]
After performing the multiplication:
[tex]\[
y \approx 18
\][/tex]
### Conclusion
- The number whose [tex]\( 14 \% \)[/tex] is 28 is approximately [tex]\( 200 \)[/tex].
- The number whose [tex]\( 16 \frac{2}{3} \% \)[/tex] is 3 is approximately [tex]\( 18 \)[/tex].
