Question

There was an equal number of dogs and cats at a party. After 8 dogs and 41 cats joined the party, there were 4 times as many cats as dogs. How many cats were at the party at first?​

Answer 1

3 cats

Explanation:

Let the initial number of dogs = number of cats = x

Number of pets = x + x = 2x

8 dogs and 41 cats joined the party

Number of dogs after the new arrivals = 8 + x

Number of cats after the new arrivals =

Total number of pets after new arrivals = 8 + x + 41 + x

= 49 + 2x

Ratio of cats to dogs after new arrivals

`(41 + x)/(8 + x) = 4`

Cross multiplying denominator with 4 on the right side:

`41 + x = 4(8 + x)\\\\41 + x = 32 + 4x\\\\41-32 = 4x - x\\\\\\9 = 3x\\\\3x = 9\\\\x = 3\\\\`

So initially there were 3 cats (and also 3 dogs) at the party