The larger of two numbers is 5 less than twice the smaller. their sum is 43. find the numbers.

Let's set up an equation.
smaller number = x
larger number = 2x - 5
Now set up the equation so that the larger number plus the smaller number adds up to 43.
x + 2x - 5 = 43
3x - 5 = 43 ( I added the x and 2x)
3x = 48 ( I added 5 to both sides)
x = 16 (I divided both sides by 3)

Now let's check it. Substitute 16 for every time there is an x.

16 + 2(16) - 5 = 43
16 + 32 - 5 = 43
48 - 5 = 43
43 = 43
It checks. x is equal to 16, so that means:
smaller number = 16
larger number = 27

Hope this helps =)