Answer:
Therefore, Mark would have eaten 127/256 of the pizza during the week.
The closest answer option to 127/256 is d) 15/16 of the pizza, which is equivalent to 240/256. Since 127/256 is less than 240/256, the correct answer is d) 15/16 of the pizza.
Explanation:
To determine how much of the pizza Mark would have eaten during the week, we need to calculate the fraction of the pizza remaining after each day.
1. On Monday, Mark ate half of the pizza, leaving 1/2 of the pizza remaining.
2. On Tuesday, Mark ate half of what was left. If there was 1/2 of the pizza remaining, he ate (1/2) * (1/2) = 1/4 of the original pizza.
3. On Wednesday, Mark ate half of what was left after Tuesday. If there was 1/4 of the pizza remaining, he ate (1/2) * (1/4) = 1/8 of the original pizza.
4. This pattern continues for the remaining days of the week.
By following this pattern for one week, Mark would have eaten a total of 1/2 + 1/4 + 1/8 + ... (continuing for a total of 7 days).
This is a geometric series with a common ratio of 1/2. The sum of a geometric series is given by the formula: S = a * (1 - r^n) / (1 - r), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1/2 (the first term), r = 1/2 (the common ratio), and n = 7 (the number of terms).
Plugging in these values into the formula, we get:
S = (1/2) * (1 - (1/2)^7) / (1 - 1/2)
Simplifying the expression, we find:
S = (1/2) * (1 - 1/128) / (1/2)
S = (1/2) * (127/128)
S = 127/256