Find two consecutive odd integers such as the sum of 4 times the larger and twice the smaller is 194

Givens

Two odd integers which can be adjusted to make 194

Let the smaller integer = 2x + 1 This guarantees that it is odd.

Let the larger integer = 2x + 3

Solve

Four times the larger = 4 (2x + 3)

Twice the smaller = 2 (2x + 1)

Sum of both = 4 (2x + 3) + 2 (2x + 1) = 194 Remove the brackets.

8x + 12 + 4x + 2 = 194 Collect Like terms

12x + 14 = 194 Subtract 14 from both sides

12x = 194 - 14

12x = 180 Divide by 12

x = 180/12

x = 15

Answer

The smaller integer = 2*15 + 1 = 30 + 1 = 31

The larger integer = 2*15 + 3 = 30 + 3 = 33

Check

Four times the larger integer = 4*33 = 132

Two times the smaller integer = 2*31 = 62

Sum 194. It checks.

Comment

I'm not sure you have to do this, but it is safest to make sure that you are adding two consecutive odd integers together. That's why we started out with 2x because that is even and then added 1 or 3 to it to make it odd.