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November 25, 2014

November 25, 2014

Posted by **ASAP PLEASE** on Wednesday, March 23, 2011 at 3:39pm.

North Pole. Ten members of the lab each

have a dog team. There are

56 dogs in all. If there are

only 7- and 5-dog teams,

how many of each will

there be

- algebra -
**tchrwill**, Thursday, March 24, 2011 at 10:20amGuess and check will get you there ultimately but I would think you are more interested in an algebraic approach.

1--Assuming there are integer solutions,

5x + 7y = 56 is what we wish to solve.

2--Divide through by the lowest coefficient yielding x + 1y + 2y/5 = 11 + 1/5

3--(2y - 1) must be an integer

4--Wanting a unit coefficient of y, multiply (2y - 1)/5 by 3 yielding (6y - 3)/5

5--DIviding by 5 again yields y + y/5 - 3/5

6--Let (y - 3)/5 = an integer k making y = 5k + 3

7--Substituuting back into (1) yields x = 7 - 7k

8--Only k = 0 will produce a meaningful integer answer of x = 7 and y = 3.

9--5(7) + 7(3) = 56

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