SOLUTION: You have 2 positive numbers. One number is one-fifth of the other number. The difference between the two numbers is 284, find the numbers.

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Question 1190212: You have 2 positive numbers. One number is one-fifth of the other number. The difference between the two numbers is 284, find the numbers.

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

x = smaller number
5x = larger number

The ratio of the two values is
smaller/larger = (x)/(5x) = 1/5
Which shows that the smaller is 1/5 of the larger
Flipped around: the larger is 5 times that of the smaller

The difference in the numbers is 284
larger - smaller = 284
5x - x = 284
4x = 284
x = 284/4
x = 71
So,
5x = 5*71 = 355

Answer:
The numbers are 71 and 355

Answer by ikleyn(52824)   (Show Source):
You can put this solution on YOUR website!
.
You have 2 positive numbers. One number is one-fifth of the other number.
The difference between the two numbers is 284, find the numbers.
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        Algebra solution

The numbers are x and 5x.

Their difference is 284:

        5x - x = 284

          4x     = 284

            x     = 284/4 = 71.

ANSWER.     The numbers are 71 and 5*71 = 355.

Solved.

        Mental solution

The difference of 284 is 4/5 of the greater number.

Hence, 1/5 of the greater number is 1/4 of 284, or 71.

It means that the greater number is 355 and the smaller number is 355:5 = 71.

You get the same answer.

                Solved twice . . .

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