On the 1st day the movie opened 35 people saw it. On the 2nd day 16 more people came than on the 1st day so that 86 people had seen the movie after the second day. On the 3rd day 67 people came, 16 more than on the 2nd day, If each day 16 more people saw the movie than the day before, on what day would 700 people have seen the movie?
Isn't this an arithemetic sequence?
distance=16, first term 35
Don't you have a formula for the sum of n terms? Use that, find n.
You are dealing with an arithmetic series.
a = 35, d=16
Sum(n) = (n/2)(2a + (n-1)d)
700 = (n/2)(70 + 16(n-1))
1400 = n(70 + 16n - 16)
1400 = 54n + 16n^2
16n^2 + 54n - 1400 =0
solve the quadratic.
But remember that n must be a positive whole number.
Also check my arithmetic, I have no pencil, paper or calculator with me at the moment.
To solve this problem, we can break it down step by step.
Let's start with the information given. On the first day, 35 people saw the movie. On the second day, 16 more people came than on the first day, resulting in a total of 86 people who have seen the movie after the second day. On the third day, 67 people came, which is 16 more than the second day.
To find out the number of people who have seen the movie each day, we can create a pattern:
Day 1: 35 people
Day 2: 35 + 16 = 51 people
Day 3: 51 + 16 = 67 people
From the pattern, we can observe that each day, the number of people who see the movie is increased by 16 compared to the previous day.
Now, let's continue with the pattern to find the number of people who have seen the movie on each subsequent day:
Day 4: 67 + 16 = 83 people
Day 5: 83 + 16 = 99 people
Day 6: 99 + 16 = 115 people
Day 7: 115 + 16 = 131 people
Using the same pattern, we can continue to find the number of people who have seen the movie on each subsequent day until we reach 700 people.
To make it more efficient, we can use an equation to find the number of days needed to reach 700 people:
Number of people on each day = 35 + (day - 1) * 16
Number of people = 700
35 + (day - 1) * 16 = 700
Solving this equation, we find:
(day - 1) * 16 = 700 - 35
(day - 1) * 16 = 665
day - 1 = 665 / 16
day - 1 = 41.5625
Since the number of days must be a whole number, we round it up to the next integer.
day = 42
Therefore, it would take 42 days for 700 people to see the movie.