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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1650 is perfect. Good work!

#1651. 90% and 97% pure acid solutions are mixed to obtain 21 liters of 95% pure acid solution. Find the amount of each type of acid to be mixed to form the mixture.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1651 is correct. Good work!

#1652. Solve : 2x + y = 5 and 3x + 2y = 8.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1652 is correct. Neat work!

#1653. Solve : x - 3y - 7 = 0 and 3x - 3y - 15 = 0.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1653 is perfect. Neat work!

#1654. Solve : 152x - 378y = -74 and -378x + 152y = -604.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1654 is correct. Excellent!

#1655. On selling a TV at 5% gain and a fridge at 10% gain, a shopkeeper gains $2000. But if he sells the TV at 10% gain and the fridge at 5% loss, he gains $1500 on the transaction. Find the actual price of the TV and fridge.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1655 is perfect. Excellent!

#1656. Solve the quadratic equation : 100x[sup]2[/sup] - 20x + 1 = 0.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1656 is correct. Perfect!

#1657. Find two numbers whose sum is 27, and product is 182.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1657 is correct. Good work!

#1658. Find the solutions of the quadratic equation : 2x[sup]2[/sup] - 7x + 3 = 0.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1658 is perfect. Neat work!

#1659. Find the roots of the equation :

, x ≠ 0Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1659 is correct. Brilliant!

#1660. The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field.

Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1660 is perfect. Good work!

#1661. Find the roots of

, x ≠ -4, 7.Character is who you are when no one is looking.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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: 14,461

Hi bobbym,

The solution #1661 is perfect. Good work!

#1662. Find the next two terms of the Arithmetic Progression :

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

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

Combinatorics is Algebra and Algebra is Combinatorics.

Offline