Question

There are 6 times as many dogs as cats. If the total number of dogs and cats is 21, how many dogs are there?

Answer 1

There are 18 dogs.

Explanation:

In questions like these it is very easy to multiply the wrong variable by 6, or whatever number, because that is what the English sounds like it is telling us.

There are `6` "TIMES AS MANY DOGS" sounds like you have to multiply the number of dogs by 6.

However, what it is actually saying is that the number of dogs is ALREADY 6 TIMES more. Do not make the number of dogs even more by multiplying that by 6.

`6` times a smaller number will be equal to a bigger number.

For example:
`30` is six times five means `6 xx 5 = 30`
We would not multiply the 30 by 6!

Let the smaller number be `x`

Let the number of cats be `x`
The number of dogs is 6 times more than the number of cats:

The number of dogs is `6x`

Together there are 21 animals:

`x+6x = 21`

`7x = 21`

`x = 3`

There are 3 cats and `6xx3 = 18` dogs