Answer :
To find the most accurate way to estimate [tex]\(35\%\)[/tex] of [tex]\(200\)[/tex], let's first understand what [tex]\(35\%\)[/tex] of [tex]\(200\)[/tex] actually is.
1. Calculate 35% of 200:
[tex]\[
35\% \text{ of } 200 = \frac{35}{100} \times 200 = 0.35 \times 200 = 70
\][/tex]
2. Evaluate each option given in terms of estimating this value:
- Option A: [tex]\(\frac{1}{4} \times 210\)[/tex]
[tex]\[
\frac{1}{4} \times 210 = 52.5
\][/tex]
- Option B: [tex]\(\frac{3}{4} \times 210\)[/tex]
[tex]\[
\frac{3}{4} \times 210 = 157.5
\][/tex]
- Option C: [tex]\(\frac{1}{2} \times 210\)[/tex]
[tex]\[
\frac{1}{2} \times 210 = 105.0
\][/tex]
- Option D: [tex]\(\frac{1}{3} \times 210\)[/tex]
[tex]\[
\frac{1}{3} \times 210 = 70.0
\][/tex]
3. Compare the results:
From our calculations, we know the true value is [tex]\(70.0\)[/tex].
- Option A gives [tex]\(52.5\)[/tex]
- Option B gives [tex]\(157.5\)[/tex]
- Option C gives [tex]\(105.0\)[/tex]
- Option D gives [tex]\(70.0\)[/tex], which matches our calculated 35% of 200.
Therefore, the most accurate estimation of [tex]\(35\%\)[/tex] of [tex]\(200\)[/tex] is given by Option D: [tex]\(\frac{1}{3} \times 210\)[/tex].
1. Calculate 35% of 200:
[tex]\[
35\% \text{ of } 200 = \frac{35}{100} \times 200 = 0.35 \times 200 = 70
\][/tex]
2. Evaluate each option given in terms of estimating this value:
- Option A: [tex]\(\frac{1}{4} \times 210\)[/tex]
[tex]\[
\frac{1}{4} \times 210 = 52.5
\][/tex]
- Option B: [tex]\(\frac{3}{4} \times 210\)[/tex]
[tex]\[
\frac{3}{4} \times 210 = 157.5
\][/tex]
- Option C: [tex]\(\frac{1}{2} \times 210\)[/tex]
[tex]\[
\frac{1}{2} \times 210 = 105.0
\][/tex]
- Option D: [tex]\(\frac{1}{3} \times 210\)[/tex]
[tex]\[
\frac{1}{3} \times 210 = 70.0
\][/tex]
3. Compare the results:
From our calculations, we know the true value is [tex]\(70.0\)[/tex].
- Option A gives [tex]\(52.5\)[/tex]
- Option B gives [tex]\(157.5\)[/tex]
- Option C gives [tex]\(105.0\)[/tex]
- Option D gives [tex]\(70.0\)[/tex], which matches our calculated 35% of 200.
Therefore, the most accurate estimation of [tex]\(35\%\)[/tex] of [tex]\(200\)[/tex] is given by Option D: [tex]\(\frac{1}{3} \times 210\)[/tex].
