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Sagot :
To determine how many tortes are left after the guests consumed a portion, we need to follow a step-by-step process:
1. Identify the Total Number of Tortes:
The chef initially prepared a total of 5 chocolate tortes.
2. Understand the Fraction of Tortes Consumed:
The guests consumed [tex]\( \frac{2 \times 5}{16} \)[/tex] tortes.
3. Simplify and Calculate the Fraction Consumed:
This fraction calculates to [tex]\( \frac{10}{16} \)[/tex], which simplifies further to [tex]\( \frac{5}{8} \)[/tex] tortes consumed.
4. Determine the Number of Tortes Left:
To find out how many tortes are left, subtract the fraction consumed from the total number of tortes:
[tex]\[ 5 - \left( \frac{5}{8} \right) \][/tex]
5. Convert the Whole Number to a Fraction:
To subtract the fractions properly, convert the whole number 5 into a fraction with the same denominator:
[tex]\[ 5 = \frac{40}{8} \][/tex]
6. Perform the Subtraction:
Now, subtract the consumed fraction from the total number converted into an equivalent fraction:
[tex]\[ \frac{40}{8} - \frac{5}{8} = \frac{35}{8} \][/tex]
7. Interpret the Result:
So, the number of tortes left is [tex]\( \frac{35}{8} \)[/tex].
Given the choices:
A. [tex]\( \frac{311}{16} \)[/tex]
B. [tex]\( \frac{3 \%}{16} \)[/tex]
C. [tex]\( \frac{29}{16} \)[/tex]
D. [tex]\( \frac{211}{16} \)[/tex]
The correct equivalent answer for [tex]\( \frac{35}{8} \)[/tex], when expressed with the same denominator used in the choices provided, is found by converting [tex]\( \frac{35}{8} \)[/tex] to have a denominator of 16:
[tex]\[ \frac{35}{8} = \frac{70}{16} \][/tex]
However, this matches none of the answers given exactly. Therefore, we must stick with the fraction we computed carefully: [tex]\( \frac{35}{8} \)[/tex].
To double-check, the fraction approximation [tex]\(4.375\)[/tex] confirms the straightforward interpretation that the fraction [tex]\( \frac{35}{8} \)[/tex] and decimals leave us with the answer fitting neither of the directly provided choices.
So, none of the provided answers [tex]\(A, B, C, \)[/tex] or [tex]\( D \)[/tex] explicitly match up when recalculated with basic arithmetic:
Therefore, from the fraction-consumed 2 [tex]\(5 / 16 \)[/tex]:
Initial preparation: 5 Tortes
Consumed equivalent approximates 0.625 or [tex]\(\frac{35}{8}\)[/tex].
Thus, our numerically calculated accurate output remains [tex]\(4.375\)[/tex]. Verifying step up suggests none matching set choices convert as derived - ideal resultant remains reapplicable as accurate leaving Computed Answer:
\(\boxed \frac{35}{8} exactly as accurate metric correct proper format applicable/none explicit reflect from choices provided respectively. Be flexible in seeing such specialized equivalences!
1. Identify the Total Number of Tortes:
The chef initially prepared a total of 5 chocolate tortes.
2. Understand the Fraction of Tortes Consumed:
The guests consumed [tex]\( \frac{2 \times 5}{16} \)[/tex] tortes.
3. Simplify and Calculate the Fraction Consumed:
This fraction calculates to [tex]\( \frac{10}{16} \)[/tex], which simplifies further to [tex]\( \frac{5}{8} \)[/tex] tortes consumed.
4. Determine the Number of Tortes Left:
To find out how many tortes are left, subtract the fraction consumed from the total number of tortes:
[tex]\[ 5 - \left( \frac{5}{8} \right) \][/tex]
5. Convert the Whole Number to a Fraction:
To subtract the fractions properly, convert the whole number 5 into a fraction with the same denominator:
[tex]\[ 5 = \frac{40}{8} \][/tex]
6. Perform the Subtraction:
Now, subtract the consumed fraction from the total number converted into an equivalent fraction:
[tex]\[ \frac{40}{8} - \frac{5}{8} = \frac{35}{8} \][/tex]
7. Interpret the Result:
So, the number of tortes left is [tex]\( \frac{35}{8} \)[/tex].
Given the choices:
A. [tex]\( \frac{311}{16} \)[/tex]
B. [tex]\( \frac{3 \%}{16} \)[/tex]
C. [tex]\( \frac{29}{16} \)[/tex]
D. [tex]\( \frac{211}{16} \)[/tex]
The correct equivalent answer for [tex]\( \frac{35}{8} \)[/tex], when expressed with the same denominator used in the choices provided, is found by converting [tex]\( \frac{35}{8} \)[/tex] to have a denominator of 16:
[tex]\[ \frac{35}{8} = \frac{70}{16} \][/tex]
However, this matches none of the answers given exactly. Therefore, we must stick with the fraction we computed carefully: [tex]\( \frac{35}{8} \)[/tex].
To double-check, the fraction approximation [tex]\(4.375\)[/tex] confirms the straightforward interpretation that the fraction [tex]\( \frac{35}{8} \)[/tex] and decimals leave us with the answer fitting neither of the directly provided choices.
So, none of the provided answers [tex]\(A, B, C, \)[/tex] or [tex]\( D \)[/tex] explicitly match up when recalculated with basic arithmetic:
Therefore, from the fraction-consumed 2 [tex]\(5 / 16 \)[/tex]:
Initial preparation: 5 Tortes
Consumed equivalent approximates 0.625 or [tex]\(\frac{35}{8}\)[/tex].
Thus, our numerically calculated accurate output remains [tex]\(4.375\)[/tex]. Verifying step up suggests none matching set choices convert as derived - ideal resultant remains reapplicable as accurate leaving Computed Answer:
\(\boxed \frac{35}{8} exactly as accurate metric correct proper format applicable/none explicit reflect from choices provided respectively. Be flexible in seeing such specialized equivalences!
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