Question

The sum of two numbers is 250 and the difference of their squares is 27,500. Find the
smaller number.​

Answer 1

Answer:

The answer to the given problem is 170.

Step-by-step explanation:

Solution:

Let the two numbers be x and y.

Given that,

$x+y=250$                     .............(1)

$x^{2} -y^{2} =27,500$            ..............(2)

By solving the 2nd equation first, we get

$x^{2} -y^{2} =27,500$

$(x-y) (x+y) =27,500$

Put the value of 1st equation i.e. $x+y=250$ , we get

$(x-y) 250= 27,500\\x-y= 27500/250\\x-y = 110$.................(3)

By solving (1) and (3)...

$x+y=250\\x-y=110$    

By eliminating y

$2x=360\\x=360/2\\x=180$

Now, put the value of x in Equation (1)

$x+y= 250\\180+y=250\\y= 250-180\\y= 170$

Hence,

the two numbers are 180 and 170.

The smaller number is 170.

#SPJ2

Answer 2

The value of the smaller number is 70.

Step-by-step explanation:

Given:

Let the two numbers be x and y.

Then their sum is x+y= 250-----(1)

Difference of their square = $x^{2} -y^{2}$= 27500

Solution:

Using the identity of the difference of squares of two numbers,

$x^{2} -y^{2}$ = (x+y)(x-y)

So putting the value of x+y= 250,

$x^{2} -y^{2}$ = 250(x-y)

27500= 250(x-y)

x-y= 27500÷250

x-y= 110----(2)

Now, solving equations 1 and 2, we get

2x=250+110

2x= 360

x= 180

Now, y= x-110

y= 70

Result:

Thus, the value of the smaller number is 70.

(#SPJ3)