Three times the smalles of theree consecutive odd numbers decreased by 7 equals twice the largest one. find the numbers

The hardest part of a word problem is translating it into the equation or equations you need. This one needs just one equation.

Let N = the smallest number. Since they are consecutive, the next ones will be N+2 and N+4. (It doesn't matter that they are odd, just that each one is 2 greater than the one before.)

So, N = the smallest number and N+4 = the largest. Translate the problem (3 times the smallest, N, decreased by 7, equals twice the largest, N+4) into numbers:

3N - 7 = 2 (N+4)

Then it's simple to find N:

3N - 7 = 2N +8

3N - 2N = 8 + 7

N = 15

The three numbers then are 15, 17, 19. Check the answer by seeing if they fit the original problem. 3 X 15 = 45, 45 - 7 = 38, 2 X 19 = 38, so we got the right values.