Randy had a sheep that started eating more and more as each day passed.On July 1,Randy’s sheep ate 5 carrots. On July 2,Randy’s sheep ate 11 carrots. On July 3, the sheep ate 18 carrots. How many carrots will the hungry sheep eat on July 30th?
Note that the differences grow by one each day. That implies a quadratic relationship. In fact
on July nth, the sheep eats n(n+9)/2 carrots.
On July 30, that's 30(39)/2 = 15*39 = 585 carrots
To determine the number of carrots the sheep will eat on July 30th, we need to find the pattern in the amount of carrots consumed each day.
From the given information, we observe that the number of carrots eaten by the sheep increases by 6 each day.
On July 1st, the sheep ate 5 carrots.
On July 2nd, the sheep ate 5 + 6 = 11 carrots.
On July 3rd, the sheep ate 11 + 6 = 17 carrots.
On July 4th, the sheep ate 17 + 6 = 23 carrots.
We can see a pattern emerging, where the number of carrots increases by 6 each day. Therefore, we can create a formula to calculate the number of carrots eaten on any given day:
Number of carrots eaten = 5 + (day - 1) * 6
Substituting day = 30 into the formula, we get:
Number of carrots eaten on July 30th = 5 + (30 - 1) * 6
= 5 + 29 * 6
= 5 + 174
= 179
Therefore, the sheep will eat 179 carrots on July 30th.
To find out how many carrots the sheep will eat on July 30th, we need to look for a pattern in the number of carrots eaten each day. Let's analyze the data provided:
On July 1, the sheep ate 5 carrots.
On July 2, the sheep ate 11 carrots.
On July 3, the sheep ate 18 carrots.
Looking at the numbers, we can observe that the number of carrots eaten each day is increasing. If we carefully examine the pattern, we can see that the increase in the number of carrots eaten each day is the result of adding consecutive odd numbers, starting from 1.
Let's list the number of carrots eaten each day and the corresponding odd numbers:
July 1: Sheep ate 5 carrots (1 + 3 + 1)
July 2: Sheep ate 11 carrots (1 + 3 + 5 + 2)
July 3: Sheep ate 18 carrots (1 + 3 + 5 + 7 + 2)
Now, let's continue this pattern to find out how many carrots the sheep will eat on July 30th:
July 30: The sheep will eat 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + ... + 55
To calculate the sum of consecutive odd numbers, we can use the formula for the sum of an arithmetic series:
Sn = (n/2) * (a + l)
Where:
Sn = Sum of the series
n = Number of terms
a = First term
l = Last term
Since we need to find the sum of consecutive odd numbers, the first term (a) is 1, the last term (l) is 55, and the common difference (d) is 2.
Using the formula, we can find the number of terms (n):
l = a + (n - 1) * d
55 = 1 + (n - 1) * 2
55 = 1 + 2n - 2
56 = 2n
n = 28
Now that we have found the number of terms (n), we can calculate the sum (Sn):
Sn = (n/2) * (a + l)
Sn = (28/2) * (1 + 55)
Sn = 14 * 56
Sn = 784
Therefore, on July 30th, Randy's sheep will eat a total of 784 carrots.