$\text{April} \times \text{May} - \text{June} = \text{December} - \text{January}$
$\text{September} \div \text{November} \times \text{December} = \text{March} \times \text{March}$
$\text{January} \times \text{February} \div (\text{February} + x ) = \text{April}$
These three equations follow a certain pattern. What month of the year fits in the spot marked $x$? Please provide a logical explanation as well.
The answer is
August
The math works as follows:
On the left side of the equation, the months represent the count of letters in their names (January = 7, February = 8, etc.).
On the right side of the equation, the months represent their location in the calendar (January = 1, February = 2, etc.).
To solve for the missing month, we have:
$ 7 \times 8 \div (8 + x) = 4$
$ 56 \div (8 + x) = 4$
$ 56 = 4(8 + x)$
$ 56 \div 4 = 8 + x$
$ 14 = 8 + x$
$ 14 - 8 = x$
$ x = 6$
The only month with
$6$ letters in its name is August, so that is the solution.
My guess:
August.
Reasoning:
The first two equations work if you replace months with the number of letters in their names on the left side of '=' and with their order in the year on the right side:
5 * 3 - 4 = 11 = 12 - 1
9 / 8 * 8 = 9 = 3 * 3
7 * 8 / (8 + _) = 4
6 is the number that fits in the gap, and August has six letters in its name.
