The product of two whole number is 462 and their sum is 43. What are the two numbers?

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:

Likewise, because their sum is 42:

This yields a system of equations:

We can solve the system using substitution.

Isolating one variable in the second equation yields:

From substitution:

Distributing yields:

Solve for b by factoring:

Solve for a:

In conclusion, the two whole numbers are 21 and 22.