| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.91 |
| Score | 0% | 58% |
If all of a roofing company's 8 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 13 | |
| 8 | |
| 10 | |
| 16 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 8 workers at the company now and that's enough to staff 2 crews so there are \( \frac{8}{2} \) = 4 workers on a crew. 6 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 6 x 4 = 24 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 24 - 8 = 16 new staff for the busy season.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 37,000 seats in a stadium are filled, how many home fans are in attendance?
| 24,000 | |
| 27,750 | |
| 33,600 | |
| 25,000 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
37,000 fans x \( \frac{3}{4} \) = \( \frac{111000}{4} \) = 27,750 fans.
What is \( \frac{2}{7} \) x \( \frac{3}{5} \)?
| \(\frac{6}{35}\) | |
| \(\frac{1}{9}\) | |
| \(\frac{1}{6}\) | |
| 1\(\frac{1}{5}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{7} \) x \( \frac{3}{5} \) = \( \frac{2 x 3}{7 x 5} \) = \( \frac{6}{35} \) = \(\frac{6}{35}\)
What is \( \frac{2}{8} \) ÷ \( \frac{3}{6} \)?
| \(\frac{3}{14}\) | |
| \(\frac{1}{18}\) | |
| \(\frac{1}{14}\) | |
| \(\frac{1}{2}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{8} \) ÷ \( \frac{3}{6} \) = \( \frac{2}{8} \) x \( \frac{6}{3} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{8} \) x \( \frac{6}{3} \) = \( \frac{2 x 6}{8 x 3} \) = \( \frac{12}{24} \) = \(\frac{1}{2}\)
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 50% of his shots. If the guard takes 20 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?
| 33 | |
| 19 | |
| 34 | |
| 25 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{50}{100} \) = \( \frac{50 x 20}{100} \) = \( \frac{1000}{100} \) = 10 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 = \( \frac{10}{\frac{30}{100}} \) = 10 x \( \frac{100}{30} \) = \( \frac{10 x 100}{30} \) = \( \frac{1000}{30} \) = 33 shots
to make the same number of shots as the guard and thus score the same number of points.