Practice Set 1 Flashcards
A physical education class has three times as many girls as boys. During a class basketball game, the girls average 18 points each, and the class as a whole averages 17 points per person. How many points does each boy score on average?
- Since the class has three times as many girls as boys, the class is composed of 75% girls and 25% boys. To find the number of points each boy scores on average, we solve the following equation: 0.7518 + 0.25X = 17, where X is the number of points each boy scores on average. Solving for X gives X = 14, so the boys average 14 points per game.
Randolph has 8 ties, 6 pairs of pants, and 4 dress shirts. How many days could he possibly go without wearing the same combination of these three items?
192 days. There are 48 different combinations of ties and shirts (8 different ties for each of the 6 pairs of pants), and then four different shirts for each of these combinations. In numerical form: 8 x 6 x 4 = 192.
John is a mechanic. He makes $8.50 an hour, plus $3 extra for every oil change he performs. Last week he worked 36 hours and performed 17 oil changes. How much money did he make?
$357. John’s base wage can be figured by multiplying his pay per hour by the number of hours he worked: $8.50 x 36 = 306. His bonus for oil changes is calculated by multiplying the payment per oil change by the number of oil changes performed: 17 x 3 = 51. These two products can then be added together.
A box of staples has a length of 6 cm, a width of 7 cm, and a volume of 378 cm cubed. What is the height of the box?
Volume is calculated as the product of length, width, and height, so if height is set as Y: 6 x 7 x Y = 378. This can be rearranged to 378 / 42 = Y = 9.
What is the average of all of the integers from 13 to 37?
This kind of problem can be easily solved by simply finding the average of the two extremes in the range: (13 + 37) / 2 = 25.
A basketball player averaged 20 points a game over the course of six games. His scores in five of those games were 23, 18, 16, 24, and 27. How many points did he score in the sixth game?
12 points.
Arnold is about to go on a 500-mile car trip. His mechanic recommends that he buy a special highway engine oil that will save him 50 cents in gas for every 25 miles of the trip. This new oil, however, will cost $20. Is it worthwhile for Arnold to buy the oil if he has a coupon for $4 dollars off the price?
No. Arnold will only save $10 by using the oil (.5 x (500 / 25)), and this is still $6 less than the cost of the oil.
