Answer:
The smaller number is 11 and the larger number is 16.
Explanation:
Let x = smaller number and y = larger number. The sum of these numbers is 27, so we can make the equation x + y = 27. Twice the smaller number (2x) plus three times the larger number (3y) is 70, so we can also make the equation 2x + 3y = 70.
Now, let's take a look at that first equation, x + y = 27. Let's isolate y on one side, giving us y = -x + 27. Now, we can replace y in the second equation with that value, which will allow us to solve for x.
2x + 3y = 70
2x + 3(-x + 27) = 70
2x - 3x + 81 = 70
-x + 81 = 70
-x = -11
x = 11
So, the smaller number is 11. Again, our original equation is x + y = 27. We can now replace x with 11.
11 + y = 27
y = 16
The larger number is 16. If you have any questions or found that really confusing, let me know and I'll try to clarify for you. :)