guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{50}{100} \) = \( \frac{50 x 10}{100} \) = \( \frac{500}{100} \) = 5 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 = \( \frac{5}{\frac{30}{100}} \) = 5 x \( \frac{100}{30} \) = \( \frac{5 x 100}{30} \) = \( \frac{500}{30} \) = 17 shots

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

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{17 + 13 + 19 + 11}{4} \) = \( \frac{60}{4} \) = 15

The number of students taking German or Spanish is 10 + 8 = 18. Of that group of 18, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 18 - 2 = 16 who are taking at least one language. 28 - 16 = 12 students who are not taking either language.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 share.

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

\( \frac{7 x 4}{6 x 4} \) + \( \frac{8 x 3}{8 x 3} \)

\( \frac{28}{24} \) + \( \frac{24}{24} \)

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

\( \frac{28 + 24}{24} \) = \( \frac{52}{24} \) = 2\(\frac{1}{6}\)

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