The sum of four consecutive counting numbers is 154. Find the smallest number:
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36
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37
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38
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31
Let the four consecutive numbers be x, x+1, x+2, x+3. Their sum is 4x + 6 = 154, so 4x = 148 and x = 37. Checking: 37 + 38 + 39 + 40 = 154. This confirms 37 is the smallest number.
To solve this problem, let's assign variables to the four consecutive counting numbers.
Let's say the smallest number is $x$.
The four consecutive counting numbers would then be $x, x+1, x+2, x+3$.
According to the problem, the sum of these four numbers is 154.
So we can write the equation:
$x + (x+1) + (x+2) + (x+3) = 154$
Now we can simplify the equation:
$4x + 6 = 154$
Subtracting 6 from both sides of the equation gives:
$4x = 148$
Dividing both sides of the equation by 4 gives:
$x = 37$
Therefore, the smallest number is 37.
The correct answer is option B.