If 35% of the town's 44,000 voters cast ballots the number of votes cast is:

(\( \frac{35}{100} \)) x 44,000 = \( \frac{1,540,000}{100} \) = 15,400

The mayor got 82% of the votes cast which is:

(\( \frac{82}{100} \)) x 15,400 = \( \frac{1,262,800}{100} \) = 12,628 votes.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

First, solve for \( \left|a - 3\right| \):

\( \left|a - 3\right| \) + 3 = -7
\( \left|a - 3\right| \) = -7 - 3
\( \left|a - 3\right| \) = -10

The value inside the absolute value brackets can be either positive or negative so (a - 3) must equal - 10 or --10 for \( \left|a - 3\right| \) to equal -10:

So, a = 13 or a = -7.

If the tiger has consumed 90 pounds of food in 9 days that's \( \frac{90}{9} \) = 10 pounds of food per day. The tiger needs to consume 150 - 90 = 60 more pounds of food to reach 150 pounds total. At 10 pounds of food per day that's \( \frac{60}{10} \) = 6 more days.