| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.73 |
| Score | 0% | 55% |
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 32,000 seats in a stadium are filled, how many home fans are in attendance?
| 26,250 | |
| 30,400 | |
| 40,833 | |
| 26,667 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
32,000 fans x \( \frac{5}{6} \) = \( \frac{160000}{6} \) = 26,667 fans.
The total water usage for a city is 5,000 gallons each day. Of that total, 23% is for personal use and 51% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 3,000 | |
| 900 | |
| 1,400 | |
| 1,200 |
51% of the water consumption is industrial use and 23% is personal use so (51% - 23%) = 28% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{28}{100} \) x 5,000 gallons = 1,400 gallons.
A bread recipe calls for 2\(\frac{3}{8}\) cups of flour. If you only have \(\frac{3}{4}\) cup, how much more flour is needed?
| 1\(\frac{3}{4}\) cups | |
| 2\(\frac{7}{8}\) cups | |
| 2\(\frac{3}{4}\) cups | |
| 1\(\frac{5}{8}\) cups |
The amount of flour you need is (2\(\frac{3}{8}\) - \(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{19}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{13}{8} \) cups
1\(\frac{5}{8}\) cups
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 14 | |
| 15 | |
| 9 | |
| 17 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{55}{100} \) = \( \frac{55 x 10}{100} \) = \( \frac{550}{100} \) = 5 shots
The center makes 35% 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 = \( \frac{5}{\frac{35}{100}} \) = 5 x \( \frac{100}{35} \) = \( \frac{5 x 100}{35} \) = \( \frac{500}{35} \) = 14 shots
to make the same number of shots as the guard and thus score the same number of points.
What is \( \frac{6}{4} \) + \( \frac{4}{8} \)?
| 1 \( \frac{3}{8} \) | |
| 2 | |
| 2 \( \frac{5}{8} \) | |
| 1 \( \frac{4}{8} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] 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 [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 2}{4 x 2} \) + \( \frac{4 x 1}{8 x 1} \)
\( \frac{12}{8} \) + \( \frac{4}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{12 + 4}{8} \) = \( \frac{16}{8} \) = 2