Question

At the warm-up event for Oscar’s All Star Hot Dog Eating Contest, Al ate one hot dog. Bob then showed him up by eating three hot dogs. Not to be outdone, Carl ate five. This continued with each contestant eating two more hot dogs than the previous contestant. How many hot dogs did Zeno (the 26th and final contestant) eat? How many hot dogs were eaten all together?

Answer 1

Zeno ate 51 hot dogs. 676 hot dogs were eaten in total.

Step-by-step explanation:

In this problem, each contestant eats two more hot dogs than the previous contestant. We can use this pattern to find out how many hot dogs Zeno ate. We start with Al who ate 1 hot dog. Then, Bob ate 3 hot dogs (1 + 2). Carl ate 5 hot dogs (3 + 2), and so on.

Zeno is the 26th and final contestant, so we can find out how many hot dogs he ate by continuing the pattern. We add 2 hot dogs for each contestant, starting from 1 (the number of hot dogs Al ate) and adding 2 for each subsequent contestant until the 26th.

Therefore, Zeno ate 1 + (2 * (26 - 1)) = 1 + (2 * 25) = 51 hot dogs.

To find out how many hot dogs were eaten all together, we can sum up the hot dogs eaten by each contestant from Al to Zeno. We can use the formula for the sum of an arithmetic series: sum = (n/2) * (first term + last term), where n is the number of terms and the first and last terms are given. In this case, n = 26, the first term = 1, and the last term = 51.

Using the formula, we find that the sum of the hot dogs eaten by all contestants is (26/2) * (1 + 51) = 13 * 52 = 676.

Answer 2

Answer:Zeno ate 51 hot dogs.

676 hot dogs were eaten all together.

Step-by-step explanation:

Al ate one hot dog. Bob then showed him up by eating three hot dogs. Not to be outdone, Carl ate five. This continued with each contestant eating two more hot dogs than the previous contestant. This means that the number of hot dogs that each contestant ate increased in an arithmetic progression.

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We want to determine the number of hot dogs eaten by the 26th contestant, T26. Therefore,

T26 = 1 + (26 - 1)2 = 1 + 50

T26 = 51 hot dogs

The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Therefore, the sum of the number of hot dogs eaten by 26 contestants, S26 would be

S26 = 26/2[2 × 1 + (26- 1)2]

S26 = 13[2 + 50)

S26 = 13 × 52 = 676 hot dogs