One positive number is one-fifth of another number. The difference between the two numbers is 164, find the numbers.

41 and 205

Step-by-step explanation:

Since the smaller number is 1/5 the larger number, the distance between the numbers is 4/5 of the larger number because (5/5 - 1/5 = 4/5).

You are given the difference, so first find the smaller number by dividing by 4:

164 = (4/5)(larger number)

164 = 4(smaller number)

41 = smaller number

Now, just multiply by 5, since 41 is 1/5 of the larger number:

41 * 5 = 205 = larger number

Optionally, check the answer by testing the difference:

205 - 41 = 164

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step-by-step explanation: