In a fund raising lottery,42% of the money collected is given as cash prizes.There are 8 cash prizes altogether.The first prize winner get #3500, the 2nd get #3100, the 3rd get #2700 and so on in arithmetical progression.
Required
(a)how much money does the 8th person get?
(b)how much prize money is there altogether?
(c)how much money was raised for the fund?
Your AP is such that a = 3500, d = -400
Person(8) = term(8) = a + 7d = 3500 + 7(-400) = 700
b) the 9th person would get 300, making that the last prize.
so total prize money is the sum of 9 terms
= (9/2)(first + last) = (9/2)(3500 + 300) = 17100
c) this represents 42% of the total raised
so .42x = 17100
x = 17100/.42 = ...
Very good
To calculate the answers to the questions, we need to follow a step-by-step process:
(a) Determining the 8th person's prize:
In this case, we are given that the cash prizes are distributed in an arithmetic progression. We can assume that the amount given to each person forms an arithmetic sequence. The first term of the sequence is #3500, and we need to determine the 8th term.
To calculate the 8th term of an arithmetic sequence, we can use the formula:
an = a + (n - 1)d
Where:
an is the nth term of the sequence,
a is the first term,
n is the position of the term we want to find (in this case, 8),
d is the common difference.
From the given information, we know that the first term, a, is #3500. We need the common difference, which we can calculate by finding the difference between the first and second terms of the sequence.
The second prize is #3100.
d = 3100 - 3500 = -400
Now we can calculate the 8th term:
a8 = 3500 + (8 - 1)(-400)
a8 = 3500 - 2800
a8 = #700
Therefore, the 8th person will receive #700.
(b) Calculating the total prize money:
Since we know there are 8 cash prizes and the first prize is #3500, we can sum up the prizes using the formula for the sum of an arithmetic sequence:
Sn = (n/2)(2a + (n-1)d)
Where:
Sn is the sum of the first n terms of the sequence,
n is the number of terms,
a is the first term,
d is the common difference.
In this case, we can plug in the values:
n = 8
a = 3500
d = -400
S8 = (8/2)(2(3500) + (8-1)(-400))
S8 = 4(7000 - 2800)
S8 = 4(4200)
S8 = #16800
Therefore, the total prize money is #16800.
(c) Determining the money raised for the fund:
We know that 42% of the money collected is given as cash prizes. This means that the total amount raised for the fund is the remaining 58% of the money collected. To calculate it, we need to solve the equation:
0.58x = #16800
Where x represents the total amount collected.
x = #16800 / 0.58
x ≈ #28965.52
Therefore, the amount of money raised for the fund is approximately #28965.52.
To summarize the findings:
(a) The 8th person will receive #700.
(b) The total prize money is #16800.
(c) The money raised for the fund is approximately #28965.52.