| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.58 |
| Score | 0% | 52% |
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 7:6 | |
| 5:6 | |
| 5:1 | |
| 49:2 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 45% 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?
| 23 | |
| 19 | |
| 18 | |
| 20 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{45}{100} \) = \( \frac{45 x 20}{100} \) = \( \frac{900}{100} \) = 9 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 = \( \frac{9}{\frac{40}{100}} \) = 9 x \( \frac{100}{40} \) = \( \frac{9 x 100}{40} \) = \( \frac{900}{40} \) = 23 shots
to make the same number of shots as the guard and thus score the same number of points.
| 1.8 | |
| 1 | |
| 2.8 | |
| 0.7 |
1
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 11 small cakes per hour. The kitchen is available for 2 hours and 33 large cakes and 190 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?
| 14 | |
| 18 | |
| 5 | |
| 11 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 33 large cakes are needed for the party so \( \frac{33}{4} \) = 8\(\frac{1}{4}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 11 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 11 x 2 = 22 small cakes during that time. 190 small cakes are needed for the party so \( \frac{190}{22} \) = 8\(\frac{7}{11}\) 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 9 + 9 = 18 cooks.
The __________ is the greatest factor that divides two integers.
least common multiple |
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greatest common multiple |
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greatest common factor |
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absolute value |
The greatest common factor (GCF) is the greatest factor that divides two integers.