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tankabanditka [31]
2 years ago
13

Kyra has a rock collection. When she puts her rocks into 2 equal plies, there are no rocks left over. When she puts her rocks in

to 3 equal piles, there are still no rocks left over. When she puts her rock into 4 equal piles, there are still no rock left over. How many rocks could kyra have?
Mathematics
1 answer:
Nat2105 [25]2 years ago
8 0

Step-by-step explanation:

According to this description we need a number that can be divided by 2,3 and 4 since the amount of rocks can be described by a natural number. However if a number is divided by 4 it is divided by 2 as well since 2*2=4.

\frac{x}{4}  =  \alpha  \\  \frac{x}{2}  = 2 \alpha

If α is a natural number then 2*α is a natural number as well as the product of two natural numbers.

Which means that we need a number devided by 3 and 4.

The smallest number that fulfills this demand is 3*4=12.

Also any product of 12 with any natural number can be devided by 3, 4 and 2.

If the exercise asks for the numbers that are divided only by 2,3 and 4 these are:

{3}^{ \alpha }  \times 12 \: and \:  {4}^{ \alpha }  \times 12 \:  \\ where \:  \alpha  \: belongs \: to \: the \: set \: of \: all \: \\ natural \: numbers

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V = 5 * 2 1/2 * 1 1/2

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V = 18 3/4cm³

Now that we know the volume, we can check each answer choice.

Option A:

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Option B:

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Option C:

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Option D:

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Therefore, the only correct options are A and B.

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