Question

Gavin's dog had a litter of puppies. All of the puppies in this litter were either yellow or black. If there was one less black puppy, the ratio of yellow puppies to black puppies would be 2/3. If there was one more black puppy, the ratio of yellow puppies to black puppies would be 1/2. How many puppies were in the litter?

Answer 1

Total number of puppies in the litter = 11

Explanation:

Let the number of yellow puppies in the litter = y

And the number of black puppies in the litter = b

If there was one less black puppy, ratio of yellow to black puppies =
`(2)/(3)`

`(y)/(b-1)=(2)/(3)`

2(b - 1) = 3y

3y - 2b = -2 -----(1)

If there was one more black puppy, ratio of yellow puppies to black puppies =
`(1)/(2)`

`(y)/(b+1)=(1)/(2)`

2y = b + 1

2y - b = 1 -------(2)

Equation (1) - 2× equation (2)

(3y - 2b) - 2(2y - b) = -2 - 2

3y - 4y - 2b + 2b = -4

y = 4

From equation (1),

3×4 - 2b = -2

12 - 2b = -2

-2b = -14

b = 7

Total number of puppies in the litter = 7 + 4 = 11