| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Ezra buys two shirts, each with a regular price of $28, how much will he pay for both shirts?
| $7.00 | |
| $49.00 | |
| $30.80 | |
| $35.00 |
By buying two shirts, Ezra will save $28 x \( \frac{25}{100} \) = \( \frac{$28 x 25}{100} \) = \( \frac{$700}{100} \) = $7.00 on the second shirt.
So, his total cost will be
$28.00 + ($28.00 - $7.00)
$28.00 + $21.00
$49.00
Simplify \( \frac{32}{52} \).
| \( \frac{2}{9} \) | |
| \( \frac{4}{9} \) | |
| \( \frac{6}{11} \) | |
| \( \frac{8}{13} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{32}{52} \) = \( \frac{\frac{32}{4}}{\frac{52}{4}} \) = \( \frac{8}{13} \)
What is the least common multiple of 3 and 9?
| 12 | |
| 25 | |
| 9 | |
| 23 |
The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [9, 18, 27, 36, 45] making 9 the smallest multiple 3 and 9 have in common.
How many hours does it take a car to travel 140 miles at an average speed of 70 miles per hour?
| 6 hours | |
| 2 hours | |
| 9 hours | |
| 3 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{140mi}{70mph} \)
2 hours
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 50% 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?
| 13 | |
| 12 | |
| 15 | |
| 8 |
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 40% 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 = \( \frac{5}{\frac{40}{100}} \) = 5 x \( \frac{100}{40} \) = \( \frac{5 x 100}{40} \) = \( \frac{500}{40} \) = 13 shots
to make the same number of shots as the guard and thus score the same number of points.