Average of 3 numbers is 87. The 2nd number is one-fourth the 1st number and 3rd number is one-fifth the 1st number. Find the difference between largest and smallest number?

To find the difference between the largest and smallest number, we need to determine the values of the three numbers first.

Let's assume the first number is x.

According to the given information, the second number is one-fourth of the first number. So, the second number can be expressed as (1/4)x.

Similarly, the third number is one-fifth of the first number. Therefore, the third number can be written as (1/5)x.

Now, we know that the average of the three numbers is 87. To find the average, we add up the three numbers and divide by 3:

(x + (1/4)x + (1/5)x) / 3 = 87

To simplify the equation, we can find a common denominator:

((20/20)x + (5/20)x + (4/20)x) / 3 = 87

Combining the terms:

(29/20)x / 3 = 87

To isolate x, we can multiply both sides of the equation by 3:

(29/20)x = 261

Now, we can solve for x by multiplying both sides by the reciprocal of (29/20), which is (20/29):

x = (261 * 20) / 29

x ≈ 180

So, the first number is approximately 180.

Now, we can find the second number by substituting the value of x into (1/4)x:

Second number = (1/4) * 180 = 45

And the third number can be found by substituting the value of x into (1/5)x:

Third number = (1/5) * 180 = 36

The largest number is 180, and the smallest number is 36.

Therefore, the difference between the largest and smallest number is:

180 - 36 = 144