if the sum of two numbers is multiplied by the first number we get 520 and if the sum is multiplied by second number we get 1080 find the smaller of two numbers

Question

please help very difficult problem for me.

Answer 1

Let the first number be x and the second be y

 

With the first scenario, we have the equation:

 

(x + y)*x = 520

 

With the second scenario, we have the equation:

 

(x + y)*y = 1080

 

In order to solve this problem we need to find a way to make one side of the first equation match one side of the second equation, preferably with only one variable on each differing side. The easiest way to do this in this situation is to solve each equation for (x + y). By doing this, you end up with these two equations:

 

(x + y) = 520/x

(x + y) = 1080/y

 

This can then be rewritten as:

 

520/x = 1080/y

 

If we multiply both sides by x and then by y we get

 

520 = 1080x/y

 

and then

 

520y = 1080x

 

solving for x we get

 

x= (520/1080)y

 

If we plug this value back into our first equation (x + y)*x = 520, we get

 

[(520/1080)y + (1080/1080)y]*(520/1080)y = 520

 

[(1600/1080)y]*(520/1080)y = 520

 

(832000/1166400)y² = 520

 

832000y² = 606528000

 

y² = 729

 

y = 27

 

Now that we have the y value, we can plug it back into the equation x= (520/1080)y to get

 

x= (520/1080)(27)

 

x = 13

 

So, in this case, the first number is 13 and the second number is 27

 

 

 

To check, simply plug these back into the two scenario equations we came up with in the beginning

 

The first scenario:

(x + y)*x = 520

 

(13 + 27)*(13) = 520

The second scenario:

(x + y)*y = 1080

 

(13 + 27)*(27) = 1080

 

I hope this helped!