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AfilCa [17]
2 years ago
9

I NEED HELP ASAP PLEASE ILL GIVE YOU MORE POINTS HELPPP!:(

Mathematics
1 answer:
mina [271]2 years ago
6 0

Answer:

1st one is 9

2nd one is 6

3rd one is 2

Step-by-step explanation:

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if the eggs in a basket are removed 2 at a time, 1 egg will remain. if the eggs are removed 3 at a time, 2 eggs will remain. if
Yanka [14]

The least number of eggs that could be in the basket is 119.

Multiple of the number:

The multiple is the numbers you get when you multiply a certain number by an integer.

Given,

If the eggs in a basket are removed 2 at a time, 1 egg will remain.

If the eggs are removed 3 at a time, 2 eggs will remain.

If the eggs are removed 4, 5, or 6 at a time, then 3, 4, and 5 eggs will remain, respectfully.

But if they are taken out 7 at a time, no eggs will be left over.

Here we need to find the least number of eggs in the basket.

Let the number of eggs in the basket be N.

We know that,

if the eggs in a basket are removed 2 at a time, one eggs will remain.

So N is 1 less than a multiple of 2, so

=> N=2A-1

If they are removed 3 at a time, 2 eggs remain.

So N is 2 more, and therefore 1 less than, a multiple of 3, so

=> N=3B-1

If the eggs are removed 4...at a time, then 3...eggs remain,

So N is 3 more, and therefore 1 less than, a multiple of 4, so

=> N=4C-1

Similarly,

For 5,

=> N = 5D - 1

For 6,

=> N = 6E - 1

So,  if they are taken out 7 at a time, no eggs will be left over.

So,

N => 7F

Where A,B,C,D,E, and F are any positive integer.

Therefore,

N = 2A-1 = 3B-1 = 4C-1 = 5D-1 = 6E-1 = 7F

Add 1 to all those:

N+1 = 2A = 3B = 4C = 5D = 6E = 7F+1

Through this,

N + 1 = 7F + 1

has to be a common multiple of 2,3,4,5,6.

So, the LCM of 2,3,4,5,6 is 60.

So N+1 is a multiple of 60 which means N is 1 less than a multiple of 60.

So we find the least multiple of 60 that is 1 more than a multiple

of 60.

The multiples are, 60, 59, ....but 59 is not a multiple of 7.

The next multiple of 60 is 120.  

1 less than 120 is 119, and sure enough, 119 is a multiple of 7.

So,

=> 119 = 17*7.

Therefore, the least number of eggs that could be in the basket is 119.

To know more about Multiple here

brainly.com/question/5992872

#SPJ4

4 0
1 year ago
What’s the solution to the system of equations
sesenic [268]

Answer:

The answer to the system of equations is 4, -4

5 0
2 years ago
Read 2 more answers
If f(x) varies directly with x and f(x)=40 when x=8, find the value of f(x) when x=2.
melamori03 [73]

f(x)=40

x=8

so if x=2 it would be 40/8 which is 5

6 0
2 years ago
Read 2 more answers
What is the product of 9 and -7?
kolezko [41]

Answer:

The product of 9 and -7 is -63

Step-by-step explanation:

Hope This Helped!

3 0
3 years ago
A butcher has 10 3/4 pounds of ground beef that will be priced at 3.40 dollars per pound. He divides the meat into 8 equal packa
spin [16.1K]
Well we know that 10 and 3/4 is equivalent to 10.75.  If we divide the meat into 8 equal packages we have to divide 10.75 by 8.  Dividing 10.75 by 8 gives us 1.34375 pounds of meat per package.  If we take that, and multiply it by our given value of $3.40 per pound, we end up getting $4.57 a package.
8 0
3 years ago
Read 2 more answers
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