On day 1, i'm going to run 12 laps at the fitrec. then, for each of the next six days, i'm going to roll a six-sided die, and th
en run that many more laps than i ran the previous day. for example, i may end up running this sequence of laps: (12, 16, 21, 22, 23, 25, 30). how many different possible 7-day sequences of this form are there?
Short answer: 36. This is a combination/permutation problem. To put it simple, a die has 6 sides, there are 7 days but 1 is already determined (12 laps). So if we multiple the options (sides on a die) × the number of days (6) we get: 6 × 6 = 36 possible outcomes.
To show this we can get 12, 13, 14, 15, 16, 17, 18 12, 13, 14, 15, 16, 17, 19 12, 13, 14, 15, 16, 17, 20 ... all the way to 12, 18, 24, 30, 36, 42, 48
First, lets write an equation that fits the data given. The string is 112 inches long. When the two pieces are cut, the first piece will be three times as long as the second piece. If we use the variable, x, to represent the second piece, we can create the following equation...
112=3x+x
Now lets solve for x.
112=4x divide both sides by 4 28 inches=x
Now we know that the second piece is 28inches long. Since the first piece is three times as long, simply multiply 28*3 and we'll know the length of the first piece.
The answer is 5 months, with the cost of $85. You can find this answer by first writing the charges as 12x + 25 and 10x + 35. Then, you set them equal to each other and solve to find x, which is the number of months. 12x + 25 = 10x + 35 - 10x 2x + 25 = 35 - 25 2x = 10 ÷ 2 x = 5
Now that we know what x is, we can substitute it in and get 10(5) + 35 = 50 + 35 = 85. I hope this helps!
