| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 39,000 seats in a stadium are filled, how many home fans are in attendance?
| 22,667 | |
| 38,333 | |
| 30,400 | |
| 29,250 |
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:
39,000 fans x \( \frac{3}{4} \) = \( \frac{117000}{4} \) = 29,250 fans.
What is \( \frac{4}{5} \) x \( \frac{3}{9} \)?
| \(\frac{4}{25}\) | |
| \(\frac{2}{45}\) | |
| \(\frac{4}{15}\) | |
| \(\frac{1}{3}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{3}{9} \) = \( \frac{4 x 3}{5 x 9} \) = \( \frac{12}{45} \) = \(\frac{4}{15}\)
If a rectangle is twice as long as it is wide and has a perimeter of 30 meters, what is the area of the rectangle?
| 50 m2 | |
| 32 m2 | |
| 8 m2 | |
| 98 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 30 meters so the equation becomes: 2w + 2h = 30.
Putting these two equations together and solving for width (w):
2w + 2h = 30
w + h = \( \frac{30}{2} \)
w + h = 15
w = 15 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 15 - 2w
3w = 15
w = \( \frac{15}{3} \)
w = 5
Since h = 2w that makes h = (2 x 5) = 10 and the area = h x w = 5 x 10 = 50 m2
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Alex buys two shirts, each with a regular price of $37, how much money will he save?
| $3.70 | |
| $11.10 | |
| $1.85 | |
| $7.40 |
By buying two shirts, Alex will save $37 x \( \frac{10}{100} \) = \( \frac{$37 x 10}{100} \) = \( \frac{$370}{100} \) = $3.70 on the second shirt.
Simplify \( \frac{16}{48} \).
| \( \frac{3}{7} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{7}{16} \) | |
| \( \frac{5}{9} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 5 factors [1, 2, 4, 8, 16] making 16 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{48} \) = \( \frac{\frac{16}{16}}{\frac{48}{16}} \) = \( \frac{1}{3} \)