posted by .

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 5-dog teams,
how many of each will
there be

  • algebra -

    Guess 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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. testing and selection of dogs

    Rolling a dog over and pinning it is a procedure that A. dogs and wolves use as a powerful discipline technique. B. trainers use to introduce themselves to a new dog. C. breeders use to establish dominance over a strange dog. D. anyone …
  2. House/ Crate training (dogs)

    please check my answer thanks which one of the following types of dogs would be easiest to train to eliminate in one spot in the yard A Lab B guard dog C Akita D Poodle I said A
  3. dog behavior

    A dog owner always says the word "coffee" to his choclate lab puppy, using no special intontion and giving no reinforcement whatsoever. Later he tries to use the work coffee as the dogs name What phenomenon would best decscrbe the …
  4. behavior problems (dogs)

    Please check my answer thanks Often, when an owner disciplines his or her dog it's done A. to help the dog understand what is expected of him. B. to teach the dog a lesson. C. in anger. D. in the best interest of the dog. I picked …
  5. English

    1. The dog is black and white. 2. The dog is blown. 3. One is a black and white dog and the other is a blown dog. 4. It's ten to twelve. 5. It's ten before twelve. 6. It's ten past twelve. 7. It's ten after five. (Are the sentences …
  6. FACS - Reading Assignment Help!

    I have this reading assignment for Family and Consumer Science. She gave us this packet for notes and to read to answer questions she gave us (that's our reading assignment which she is grading). So we answer the questions and to find …
  7. Math

    16. Alison uses a total of 94.5 cups of dog food each week to feed her three dogs. Each dog eats the same amount. How much does each dog eat in one day?
  8. Biology- Scientific Method

    An experimenter sets out to find out how many hours of sleep a dog needs in order to catch the highest number of balls without a bounce. To test this the experimenter uses 5 dogs in the experiment and allows each dog to sleep a predetermined …
  9. animals

    A stray dog used to bark at the locals in the street. However each time whenever the person who is barked at, approached the dog, it would run away cowardly. a.Why does the dog keeps on barking in a threatening manner whereas it is …
  10. Physics

    1. A dog sits under the only shade tree in its territory. Suddenly the dog desires to dig a previously buried bone. From the tree the dog goes 13 meters at 22.6° north of east. Not finding the bone there the dog then goes 17 meters …

More Similar Questions