To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{5} \) x \( \frac{2}{7} \) = \( \frac{3 x 2}{5 x 7} \) = \( \frac{6}{35} \) = \(\frac{6}{35}\)

There are 2 2-passenger taxis available so that's 2 x 2 = 4 total seats. There are 5 people needing transportation leaving 5 - 4 = 1 who will have to find other transportation.

By buying two shirts, Charlie will save $42 x \( \frac{10}{100} \) = \( \frac{$42 x 10}{100} \) = \( \frac{$420}{100} \) = $4.20 on the second shirt.

So, his total cost will be
$42.00 + ($42.00 - $4.20)
$42.00 + $37.80
$79.80

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 2}{8 x 2} \) - \( \frac{6 x 1}{16 x 1} \)

\( \frac{14}{16} \) - \( \frac{6}{16} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{14 - 6}{16} \) = \( \frac{8}{16} \) = \(\frac{1}{2}\)