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## Explanation

The sum of two numbers is 184.

If one-third of the one exceeds one-seventh of the other by 8, the smaller number can be figure out as follows.

Let suppose two numbers are “y and z”. Their sum is 184.

y + z = 184 ________ (i)

One-third of the one (y/3) exceeds one-seventh of the other (z/7) by 8.

y/3 – 8 = z/7 ________ (ii)

Through equation (i) and (ii), we can find out the smaller number.

## To Find

Smaller number = ?

## Solution

Let suppose

Numbers = y and z

Now; according to given condition

y + z = 184 ________ (1)

y/3 – 8 = z/7

y/3 – z/7 = 8

7y – 3z = 168 ________ (2)

Multiplying equation (1) with 3

3y + 3z = 552 ________ (3)

Now adding equation (2) and (3);

7y + 3y – 3z + 3z = 168 + 552

10y = 720

y = 72 putting in equation (1)

72 + z = 184

z = 184 – 72

z = 112

So,

**Smaller number = 72 answer**

## Conclusion

The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, the smaller number would be 72.