The three numbers whose sum is 57, difference of largest and smallest number is 52 and the sum of two smaller numbers is 13 are: -8, 21, and 44
You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
We can assume that:
The numbers are x, y and z
It is given that there is positive difference between largest and smallest number, that means they're not all same.
So let we take:
x ≤ y < z (the ≤ between x and y shows that we're still not sure whether y is bigger than x or equal, but we assumed the value of x is going to be the smallest).
Now, from the description given, we get three equations as:
[tex]x+y+z = 57[/tex] (The sum of three numbers is 57)
[tex]z - x = 52[/tex] (The difference of the largest and the smallest is 52)
[tex]x+y = 13[/tex] (the sum of two smaller numbers is 13)
That gives us x ≠ y since addition of two equal numbers is always even.
From the second equation, we get:
[tex]z -x = 52\\z = x+52[/tex]
From the third equation, we get:
[tex]x+y = 13\\y = 13-x[/tex]
Putting these two expressions in place of y and z in the first equation, we get:
[tex]x+y+z = 57 \implies x +(13-x) + 52+x = 57\\65 + x = 57\\x = 57 - 65 = -8[/tex]
Therefore, we get:
[tex]z= x + 52 = -8 + 52 = 44[/tex]
[tex]y = 13 -x = 13 - (-8) = 21[/tex]
Thus, the three numbers the problem is talking about are -8, 21, and 44
Learn more about forming equations here:
https://brainly.com/question/11938672
