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inn [45]
3 years ago
6

There were 63 equal piles of plantain fruit put together and 7 single fruits. They were divided evenly among 23 travelers. What

is the number of fruits in each pile? (Hint: Consider the diophantine equation 63x + 7 = 23y.
Mathematics
1 answer:
antiseptic1488 [7]3 years ago
7 0

Answer:

There are 28 fruits in each pile.

Step-by-step explanation:

We are given the following in the question:

Let x denote the number of fruits in each pile and y denote the number of fruits that every traveler receive.

Consider the diophantine equation:

63x + 7 = 23y\\63x-23y = -7

We obtain the greatest common divisor of (63,-23).

The greatest common divisor f 63 and -23 is 1.

Therefore, there exist \alpha,\beta such that

-23\alpha+63\beta=1

By applying extended Euclidean Algorithm, we have,

1 = (1\times 6)+(-1\times 5)\\1 = (1\times 17)+(3\times 6)\\1 = (3\times 23)+(-4\times 17)\\1 = (-4\times 40)+(7\times 23)\\1 = (7\times 63)+(-11\times 40)\\1 = (-11\times -23)+(-4\times 63)

1 = (-11\times -23) + (-4\times 63)

Multiplying -7 on both sides, we get,

-7 = (77\times -23) + 28\times 63)

Thus, we get,

x = 28\\y=77

Thus, there are 28 fruits in each pile.

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Find the x-intercepts of f(x) = x2 + 7x + 10.
Andrej [43]

Answer:

x = - 5, x = - 2

Step-by-step explanation:

Given

f(x) = x² + 7x + 10

To find the x- intercepts let f(x) = 0, that is

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3 years ago
Question 7 of 10
klemol [59]
I think the answer is C. 45 units
4 0
2 years ago
Alyssa, Bart and Meghan are
adoni [48]

Hi,

Essentially, we are saying that Alyssa gets 5 parts of the whole thing (140,000), Bart gets 3 parts of the whole and Meghan gets 2 parts of the whole. The sum total of their parts = the whole. So now we need to find out how much one part is. Thus,"one part" should be the variable. Substitute p for "one part", so Alyssa gets 5p, Bart gets 3p, and Meghan gets 2p. Since the sum of the parts = the whole, your problem sets up as:  5p + 3p + 2p = 140,000  -->  10p = 140,000 --> 10p/10 = 140,000/10  -->  x = 14,000.

Alyssa gets 5p or (5 x 14,000)

Bart gets 3p or (3 x 14,000)

Meghan gets 2p or (2 x 14,000)

If the whole was a loss, it would be a negative, and instead of getting money, they would lose money.

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Step-by-step explanation:

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