If three times the sum of two, numbers is 42 and five times their difference is 20, find the numbers

The two numbers are 5 and 9.

Explanation:

Given the information in the problem, if three times the sum of two numbers is 42, we can attempt to work backwards by doing the opposite of "three times the sum", which is dividing 42 by 3:

We've figured out that the sum of these two numbers is 14.

Again, given the information in the problem, five times the difference of these two numbers is 20. Now, the only number that can multiply by 5 to get 20, is 4. We have to think of two numbers that will both, add up to 14, and when subtracted, have a difference of 4.

We can conclude that our two numbers are:

&

-

To check your work, run through the problem and simulate the given processes:

(First: Three times the sum of two numbers = 42)

(Second: Five times their difference is 20)

Therefore, our solution is correct!

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