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Answer :
To find the most accurate way to estimate [tex]\(59\%\)[/tex] of [tex]\(161\)[/tex], let's break down the options:
1. Actual Calculation: We start by calculating the actual value of [tex]\(59\%\)[/tex] of [tex]\(161\)[/tex]:
[tex]\[
0.59 \times 161 = 94.99
\][/tex]
2. Estimates:
- Option 1: [tex]\(\frac{9}{10} \times 160 = 144.0\)[/tex]
- Option 2: [tex]\(\frac{3}{5} \times 170 = 102.0\)[/tex]
- Option 3: [tex]\(\frac{3}{5} \times 160 = 96.0\)[/tex]
- Option 4: [tex]\(\frac{9/10} \times 170 = 153.0\)[/tex]
3. Calculate the Difference: We need to determine which estimate is closest to the actual value of [tex]\(94.99\)[/tex].
- Difference for Option 1: [tex]\(|94.99 - 144.0| = 49.01\)[/tex]
- Difference for Option 2: [tex]\(|94.99 - 102.0| = 7.01\)[/tex]
- Difference for Option 3: [tex]\(|94.99 - 96.0| = 1.01\)[/tex]
- Difference for Option 4: [tex]\(|94.99 - 153.0| = 58.01\)[/tex]
4. Conclusion: Option 3, which is [tex]\(\frac{3}{5} \times 160\)[/tex], gives us a value of [tex]\(96.0\)[/tex]. The difference between this value and the actual [tex]\(59\%\)[/tex] of [tex]\(161\)[/tex] (which is [tex]\(94.99\)[/tex]) is just [tex]\(1.01\)[/tex]. This is the smallest difference compared to the other options.
Therefore, the most accurate way to estimate [tex]\(59\%\)[/tex] of [tex]\(161\)[/tex] is [tex]\(\frac{3}{5} \times 160\)[/tex].
1. Actual Calculation: We start by calculating the actual value of [tex]\(59\%\)[/tex] of [tex]\(161\)[/tex]:
[tex]\[
0.59 \times 161 = 94.99
\][/tex]
2. Estimates:
- Option 1: [tex]\(\frac{9}{10} \times 160 = 144.0\)[/tex]
- Option 2: [tex]\(\frac{3}{5} \times 170 = 102.0\)[/tex]
- Option 3: [tex]\(\frac{3}{5} \times 160 = 96.0\)[/tex]
- Option 4: [tex]\(\frac{9/10} \times 170 = 153.0\)[/tex]
3. Calculate the Difference: We need to determine which estimate is closest to the actual value of [tex]\(94.99\)[/tex].
- Difference for Option 1: [tex]\(|94.99 - 144.0| = 49.01\)[/tex]
- Difference for Option 2: [tex]\(|94.99 - 102.0| = 7.01\)[/tex]
- Difference for Option 3: [tex]\(|94.99 - 96.0| = 1.01\)[/tex]
- Difference for Option 4: [tex]\(|94.99 - 153.0| = 58.01\)[/tex]
4. Conclusion: Option 3, which is [tex]\(\frac{3}{5} \times 160\)[/tex], gives us a value of [tex]\(96.0\)[/tex]. The difference between this value and the actual [tex]\(59\%\)[/tex] of [tex]\(161\)[/tex] (which is [tex]\(94.99\)[/tex]) is just [tex]\(1.01\)[/tex]. This is the smallest difference compared to the other options.
Therefore, the most accurate way to estimate [tex]\(59\%\)[/tex] of [tex]\(161\)[/tex] is [tex]\(\frac{3}{5} \times 160\)[/tex].
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