| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.06 |
| Score | 0% | 61% |
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Roger buys two shirts, each with a regular price of $44, how much will he pay for both shirts?
| $39.60 | |
| $48.40 | |
| $4.40 | |
| $83.60 |
By buying two shirts, Roger will save $44 x \( \frac{10}{100} \) = \( \frac{$44 x 10}{100} \) = \( \frac{$440}{100} \) = $4.40 on the second shirt.
So, his total cost will be
$44.00 + ($44.00 - $4.40)
$44.00 + $39.60
$83.60
What is the greatest common factor of 68 and 80?
| 4 | |
| 47 | |
| 12 | |
| 28 |
The factors of 68 are [1, 2, 4, 17, 34, 68] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 3 factors [1, 2, 4] making 4 the greatest factor 68 and 80 have in common.
The __________ is the greatest factor that divides two integers.
greatest common factor |
|
greatest common multiple |
|
absolute value |
|
least common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.
What is \( \frac{3}{4} \) - \( \frac{7}{6} \)?
| 1 \( \frac{6}{9} \) | |
| -\(\frac{5}{12}\) | |
| \( \frac{5}{12} \) | |
| 2 \( \frac{2}{7} \) |
To subtract 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 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 3}{4 x 3} \) - \( \frac{7 x 2}{6 x 2} \)
\( \frac{9}{12} \) - \( \frac{14}{12} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{9 - 14}{12} \) = \( \frac{-5}{12} \) = -\(\frac{5}{12}\)
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 14 small cakes per hour. The kitchen is available for 4 hours and 24 large cakes and 460 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 7 | |
| 11 | |
| 14 | |
| 8 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 24 large cakes are needed for the party so \( \frac{24}{12} \) = 2 cooks are needed to bake the required number of large cakes.
If a single cook can bake 14 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 14 x 4 = 56 small cakes during that time. 460 small cakes are needed for the party so \( \frac{460}{56} \) = 8\(\frac{3}{14}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 9 = 11 cooks.