Question: The sum of two numbers is 59. If the smaller number is less than the bigger one by 7, find the number.

Solution:

Let the bigger number be 'x' and the smaller number be 'y'.

According to the question,

Condition I,

The sum of two numbers is 59. $or, x + y = 59$
$or, x = 59 - y$ - (i)

Condition II,

The smaller number is less than the bigger one by 7. $or, x = y +7$ - (ii)

Put value of x from equation (i) in equation (ii), we get,

$or, 59 - y = y +7$
$or, 59 - 7 = y +y$
$or, 52 = 2y$
$or, 2y = 52$
$or, y = \frac{52}{2}$
$\therefore y = 26$

Now,

Put the value of y in equation (i), we get,

$or, x = 59 - 26$
$\therefore x = 33$

So, (x,y) = (33,26)

Hence, the required greater number is 33 and the required smaller number is 26 that fulfills the given two conditions.

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