Question

There are seven cats in my neighborhood, with an average of $41$ whiskers each. If one of the cats has $17$ whiskers, how many whiskers does each of the other cats have on average?

Answer 1

45

Explanation:

Solution #1

Let W be the total number of whiskers among all seven cats. Then we know that W/7 = 41, so W = 7 ∙ 41 = 287. If we remove the cat with 17 whiskers from consideration, then we have six other cats with a total of 287 - 17 = 270 whiskers, so their average number of whiskers is 270/6 = 45.

Solution #2

We can use the concept of "balancing". The cat with 17 whiskers has 24 fewer whiskers than average (since 41 - 17 = 24). Therefore, the other six cats must have a total of 24 more whiskers than six average cats. That's an average of 24/6 = 4 extra whiskers per cat, so these six cats have an average of 45 whiskers each.

Answer 2

Each of the other cats have 45 whiskers on average.

Explanation:

Let x represent the average number of whisker of each cat.

We have been given that there are 7 cats in my neighborhood, with an average of 41 whiskers each.

The total number of whiskers of six cats would be
`6x`.

Since one of the cats has 17 whiskers, so the total number of whiskers of 7 cats would be
`6x+17`

We will use average formula to solve our given problem.

`\text{Average}=\frac{\text{Sum of data points}}{\text{Number of data points}}`

Upon substituting our given values, we will get:

`41=(6x+17)/(7)`

Let us solve for x.

`41*7=(6x+17)/(7)*7`

`287=6x+17`

`287-17=6x+17-17`

`270=6x`

Switch sides:

`6x=270`

`(6x)/(6)=(270)/(6)`

`x=45`

Therefore, the each of the other cats have 45 whiskers on average.