Question
If three times the first of three consecutive odd integers is added to twice the second, the result is 47. Find the integers.
If three times the first of three consecutive odd integers is added to twice the second, the result is 47. Find the integers.
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Koala Tutor
Koala Ai Support
Let's assume that the first odd integer is $x$. Therefore, the second odd integer would be $x+2$, and the third odd integer would be $x+4$.
According to the given condition, three times the first odd integer is equal to twice the second odd integer plus $47$: $$3x = 2(x+2) + 47$$
Simplifying the equation, we have: $$3x = 2x + 4 + 47$$ $$3x = 2x + 51$$
Subtracting $2x$ from both sides, we get: $$x = 51$$
Therefore, the first odd integer is $51$, the second odd integer is $51+2=53$, and the third odd integer is $51+4=55$.