-If A and B are two different numbers selected from the first thirty counting numbers from 1 to 30 inclusive, what is the largest possible value of A+B/ A-B?
-Ann takes medicine for a cold. She must take one pill every 8 hours and a teaspoonful of cough medicine every 5 hours. There are 31 pills. She starts by taking a pill and the cough medicine at the same time. She takes her pills and cough medicine as stated until the 31 pills have been taken. How many times (including the first) will the pill and cough medicine be taken at the same time?
you want the largest possible numerator and the smallest possible denominator:
A=30
B=29
(A+B)/(A-B) = 59
They are taken together every 40 hours.
30*8 = 240 min
In 240/40=6, so they go together 7 times.
(adding in the first pill)
how did you get 40 hours?
To find the largest possible value of A+B/ A-B, we need to consider the values of A and B that will result in the highest value for the expression.
The first step is to determine the maximum possible value for A and B. In this case, it is the first thirty counting numbers from 1 to 30 inclusive.
Next, we need to consider the expression A+B/ A-B. The division operation (/) takes precedence over addition and subtraction, so we should calculate A+B first and then divide the result by A-B.
To maximize the expression, we want A+B to be as large as possible and A-B to be as small as possible.
Since A and B are different numbers selected from the first thirty counting numbers, let's consider the maximum and minimum values for A and B:
The maximum value for A is 30, and the minimum value for B is 2 (since they are different numbers).
So, the maximum value for A+B is 30+2=32.
The minimum value for A-B is 30-2=28.
Now, we can calculate the expression:
(A+B)/ (A-B) = 32/28 = 1.1428571428571428
Therefore, the largest possible value of A+B/ A-B is approximately 1.1428571428571428.
Now, let's move on to the second question.
To determine how many times the pill and cough medicine will be taken at the same time, we need to consider the intervals at which Ann takes each.
The pill is taken every 8 hours, and the cough medicine is taken every 5 hours. To find the time at which both will be taken simultaneously, we need to find the least common multiple (LCM) of 8 and 5.
The LCM of 8 and 5 is 40.
This means that after 40 hours, both the pill and cough medicine will be taken together again.
Since Ann takes the medicine for a total of 31 pills, we need to determine how many times the pill and cough medicine will be taken at the same time within this time frame.
Dividing the total time (31 pills * 40 hours) by the time interval (40 hours) gives us the answer:
31*40/40 = 31
Therefore, the pill and cough medicine will be taken at the same time 31 times (including the first time).