Sure, let's go through each part step by step.
### Part (i)
We need to find the product of two mixed numbers: [tex]\( 6 \frac{1}{8} \)[/tex] and [tex]\( 15 \frac{3}{4} \)[/tex].
1. Convert the mixed numbers to improper fractions:
- For [tex]\( 6 \frac{1}{8} \)[/tex]:
[tex]\[
6 \frac{1}{8} = 6 + \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{49}{8}
\][/tex]
- For [tex]\( 15 \frac{3}{4} \)[/tex]:
[tex]\[
15 \frac{3}{4} = 15 + \frac{3}{4} = \frac{15 \times 4 + 3}{4} = \frac{63}{4}
\][/tex]
2. Multiply the improper fractions:
[tex]\[
\text{Product} = \frac{49}{8} \times \frac{63}{4} = \frac{49 \times 63}{8 \times 4} = \frac{3087}{32}
\][/tex]
3. Convert the result back to a mixed number (optional):
[tex]\[
\frac{3087}{32} = 96.46875
\][/tex]
Thus, [tex]\( 6 \frac{1}{8} \)[/tex] of [tex]\( 15 \frac{3}{4} \)[/tex] is [tex]\( 96.46875 \)[/tex].
### Part (ii)
We need to solve for [tex]\( x \)[/tex] if [tex]\( 8.4\% \)[/tex] of [tex]\( x \)[/tex] is 420.
1. Understand the percentage relationship:
[tex]\[
8.4\% \text{ of } x = 420
\][/tex]
2. Convert the percentage to a decimal:
[tex]\[
8.4\% = \frac{8.4}{100} = 0.084
\][/tex]
3. Set up the equation from the percentage problem:
[tex]\[
0.084 \times x = 420
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{420}{0.084} = 5000
\][/tex]
Thus, [tex]\( x \)[/tex] is [tex]\( 5000 \)[/tex].
### Summary
1. [tex]\( 6 \frac{1}{8} \)[/tex] of [tex]\( 15 \frac{3}{4} \)[/tex] is [tex]\( 96.46875 \)[/tex].
2. The value of [tex]\( x \)[/tex] if [tex]\( 8.4\% \)[/tex] of [tex]\( x \)[/tex] is 420 is [tex]\( 5000 \)[/tex].
