algebra
posted by ASAP PLEASE .
A research lab is planning to explore the
North Pole. Ten members of the lab each
have a dog team. There are
56 dogs in all. If there are
only 7 and 5dog teams,
how many of each will
there be

Guess and check will get you there ultimately but I would think you are more interested in an algebraic approach.
1Assuming there are integer solutions,
5x + 7y = 56 is what we wish to solve.
2Divide through by the lowest coefficient yielding x + 1y + 2y/5 = 11 + 1/5
3(2y  1) must be an integer
4Wanting a unit coefficient of y, multiply (2y  1)/5 by 3 yielding (6y  3)/5
5DIviding by 5 again yields y + y/5  3/5
6Let (y  3)/5 = an integer k making y = 5k + 3
7Substituuting back into (1) yields x = 7  7k
8Only k = 0 will produce a meaningful integer answer of x = 7 and y = 3.
95(7) + 7(3) = 56