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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi anonimnystefy and bobbym,

The solutions #4419 and #4420 are correct. Excellent!

#4421. Express each number as a product of its prime factors:

(a) 140

(b) 156

(c) 3825

(d) 5005

(e) 7429

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutios (a), (b), (c), and (d) are correct. Excellent!

The solution (e)

#4422. Find the Least Common Multiple and Greatest Common Divisor of the following pairs of integers and verify that

LCM x GCD = product of the two numbers.

(a) 26 and 91

(b) 510 and 92

(c) 336 and 54

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi ganesh;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solution(s) #4422 is/are correct. Good work!

#4423. The Least Common Multiple of two numbers is 64699, and their Greatest Common Divisor is 97. One of the numbers is 2231. Find the other.

#4424. The product of two numbers is 20736 and their Greatest Common Divisor is 54. Find their Least Common Multiple.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solution #4423 is correct. Neat work!

#4425. Solve the following system of equations : x + y = 7; 2x - 3y = 11.

#4426. Solve : 2x - 7y = 1 and 4x + 3y = 15.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4425 and #4426 are correct. Neat work!

#4427. Solve : 3x + 5y = 7 and 11x - 13y = 9.

#4428. Solve : 2x - y = 11 and 5x + 4y = 1.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4427 and #4428 are correct. Excellent!

#4429. Solve : 3x - 5y - 4 = 0 and 9x = 2y + 7.

#4430. Solve : x/2 + 2y/3 = -1 and x - y/3 = 3.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4429 and #4430 are correct. Neat work!

#4431. Solve :

#4432. Solve :

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4431 and #4432 are correct. Brilliant!

#4433. Solve :

#4434. Solve :

.Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi ganesh;

Do not worry about the error.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4433 and #4434 are correct. Neat work!

#4435. Solve :

#4436. Solve : 6x + 3y = 6xy and 2x + 4y = 5xy.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4435 and #4436 are correct. Marvelous!

#4437. Solve :

#4438. Solve :

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4437 and #4438 are correct. Brilliant!

#4439. Solve : 35x + 23y = 209 and 23x + 35y = 197.

#4440. Solve : 4/x + 5y = 7 and 3/x + 4y = 5.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi ganesh;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4439 and #4440 are correct. Smart work!

#4441. Solve :

.#4442. Solve :

.Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

Hi;

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,534

Hi bobbym,

The solutions #4441 and #4442 are perfect. Outstanding!

#4443. Seven times a two-digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3, find the number.

#4444. A takes 3 hours more than B to cover distance of 30 kilometers. But, if A doubles his speed he is ahead of B by 90 minutes; find their speeds of walking.

Character is who you are when no one is looking.

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