Find two consecutive odd integers such that the sum of four times the larger and twice the smaller is 194.
Please help! Thank you!
To solve this problem, let's break it down into steps:
Step 1: Identify the unknowns
Let's assume the first odd integer is x. Since we are looking for consecutive odd integers, the next odd integer will be x + 2.
Step 2: Set up the equation
According to the problem, the sum of four times the larger and twice the smaller is 194. We can write this as an equation:
4(x + 2) + 2x = 194
Step 3: Solve the equation
Now, let's solve the equation for x:
4(x + 2) + 2x = 194
4x + 8 + 2x = 194
6x + 8 = 194
6x = 194 - 8
6x = 186
x = 186 / 6
x = 31
Step 4: Find the consecutive odd integers
We found that x = 31. So, the first odd integer is 31. The next odd integer can be found by adding 2 to it: 31 + 2 = 33.
Therefore, the two consecutive odd integers that satisfy the given condition are 31 and 33.