Answer:
21 and 22
Step-by-step explanation:
Let the two whole numbers be a and b.
Their product is 462. Hence, we can write that:
[tex]ab=462[/tex]
Likewise, because their sum is 42:
[tex]a+b=43[/tex]
This yields a system of equations:
[tex]\displaystyle \begin{cases} ab = 462 \\ a + b = 43 \end{cases}[/tex]
We can solve the system using substitution.
Isolating one variable in the second equation yields:
[tex]a=43-b[/tex]
From substitution:
[tex](43-b)(b)=462[/tex]
Distributing yields:
[tex]-b^2+43b=462[/tex]
Solve for b by factoring:
[tex]\displaystyle \begin{aligned} b^2 - 43d & = -462 \\ \\ b^2 - 43d + 462 & = 0 \\ \\ (b-21)(b-22) &= 0 \\ \\ b = 21 \text{ or } b & = 22 \end{aligned}[/tex]
Solve for a:
[tex]\displaystyle \begin{aligned} a& =43-(21) & \text{ or } a& =43-(22) \\ a&=22&\text{ or } a&=21\end{aligned}[/tex]
In conclusion, the two whole numbers are 21 and 22.
