The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

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

First, solve for \( \left|b + 3\right| \):

\( \left|b + 3\right| \) + 4 = -2
\( \left|b + 3\right| \) = -2 - 4
\( \left|b + 3\right| \) = -6

The value inside the absolute value brackets can be either positive or negative so (b + 3) must equal - 6 or --6 for \( \left|b + 3\right| \) to equal -6:

So, b = 3 or b = -9.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{15}{\frac{50}{100}} \) = 15 x \( \frac{100}{50} \) = \( \frac{15 x 100}{50} \) = \( \frac{1500}{50} \) = 30 shots

to make the same number of shots as the guard and thus score the same number of points.

If the tiger has consumed 48 pounds of food in 8 days that's \( \frac{48}{8} \) = 6 pounds of food per day. The tiger needs to consume 78 - 48 = 30 more pounds of food to reach 78 pounds total. At 6 pounds of food per day that's \( \frac{30}{6} \) = 5 more days.