the 6th grade has 5 days to sell tickets to a talent show. The students predict that each day they will sell 10 fewer tickets than the day before. How many must they sell on the first day if they want to sell 200 tickets?
--- do I divide 10 by 200 that would not make sense
please try to help me thanks
You are probably studying arithmetic sequences and series
let the first term be a
common difference is -10
and the number of terms is 5
Sn = (n/2)[2a + (n-1)d]
200 = (5/2)[2a + 4(-10)]
400 = 5[2a - 40]
400 = 10a - 200
600 = 10a
a = 60
So on the first day they must sell 60 tickets
check: 60 + 50 + 40 + 30 + 20 =
assume that they will sell x tickets on the first day.
Sale on second day will be x-10
third day x-20
fourth day x-30
fifth day x-40
if we add them all up
x+x-10+x-20+x-30+x-40=200
5x-100=2==
5x=300
x=60
so they have to sell 60 on the first day
50 on the second
40 on the third
30 on the fourth
and 20 on fifth day.
To solve this problem, let's start by setting up an equation. Let's call the number of tickets they sell on the first day "x".
According to the problem, each day they sell 10 fewer tickets than the day before. So, the number of tickets they sell on the second day would be (x - 10), on the third day it would be ((x - 10) - 10), and so on.
We know that they have 5 days in total to sell the tickets. So, the equation can be written as:
x + (x - 10) + ((x - 10) - 10) + (((x - 10) - 10) - 10) + ((((x - 10) - 10) - 10) - 10) = 200
Simplifying this equation, we get:
x + x - 10 + x - 10 - 10 + x - 10 - 10 - 10 + x - 10 - 10 - 10 - 10 = 200
Combining like terms, we have:
5x - 40 = 200
Adding 40 to both sides of the equation, it becomes:
5x = 240
Finally, dividing both sides by 5 yields:
x = 48
Therefore, they must sell 48 tickets on the first day if they want to sell a total of 200 tickets over 5 days.