If a single cook can bake 3 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 3 x 2 = 6 large cakes during that time. 34 large cakes are needed for the party so \( \frac{34}{6} \) = 5\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 12 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 12 x 2 = 24 small cakes during that time. 150 small cakes are needed for the party so \( \frac{150}{24} \) = 6\(\frac{1}{4}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 6 + 7 = 13 cooks.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 6 factors [1, 2, 3, 4, 6, 12] making 12 the greatest factor 24 and 36 have in common.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{45}{100} \) = \( \frac{45 x 20}{100} \) = \( \frac{900}{100} \) = 9 shots

The center makes 30% 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 = \( \frac{9}{\frac{30}{100}} \) = 9 x \( \frac{100}{30} \) = \( \frac{9 x 100}{30} \) = \( \frac{900}{30} \) = 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 120 pounds of food in 8 days that's \( \frac{120}{8} \) = 15 pounds of food per day. The tiger needs to consume 180 - 120 = 60 more pounds of food to reach 180 pounds total. At 15 pounds of food per day that's \( \frac{60}{15} \) = 4 more days.