Answer:
26 and 36.
Step-by-step explanation:
Let the two whole numbers be a and b. Thus, the product of them is 936 while their sum is 62. In equations, this is:
[tex]ab=936\\a+b=62[/tex]
This is a system of equations. To solve, subtract either a or b from the second equation and substitute it into the first.
For instance, subtract b from both sides in the second equation:
[tex]a+b=62\\a=62-b[/tex]
Substitute this into the first equation:
[tex](62-b)(b)=936[/tex]
Distribute:
[tex]62b-b^2=936[/tex]
Rearrange:
[tex]-b^2+62b=936[/tex]
Divide everything by -1 to make the leading coefficient positive:
[tex]b^2-62b=-936[/tex]
Add 936 to both sides:
[tex]b^2-62b+936=0[/tex]
This is now a quadratic. Solve for b.
To do so, we can factor.
After a bit of testing, we can see that -36 and -26 are possible. Thus:
[tex](b-26)(b-36)=0[/tex]
For for b:
[tex]b=26\text{ or } b=36[/tex]
Thus, b is 26 or 36.
Now, plug these back into the isolated equation to solve for a:
[tex]a=62-b\\a=62-(26) \text{ or } a=62-(36)\\a=36\text{ or } a=26[/tex]
It doesn't really matter which one we choose since they're the same.
Thus, the answer is 26 and 36.
