Monica scored 87% on the test meaning she earned 87% of the possible points on the test. There were 90 possible points on the test so she earned 90 x 0.87 = 78 points. Each question is worth 3 points so she got \( \frac{78}{3} \) = 26 questions right.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{64}{64}} \)
\( \frac{\sqrt{64}}{\sqrt{64}} \)
\( \frac{\sqrt{8^2}}{\sqrt{8^2}} \)
1

To fill a 16 gallon tank exactly halfway you'll need 8 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{8 \text{ gallons}}{2 \text{ gallons}} \) = 4

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.

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.