A church group has a fund raiser in which they raise $2,040.00. If there were 69 more people then everyones donations would be $23.00 less. How many members were there originally and how much did they donate?
let n be the number of folks
let D be the donation per person
n*D=2040
(n+69)(d-23)=2040
With those two equations, it ought to work out. Repost if you have difficulties.
I've studied this several ways.
There are a few different equations that can be defined to represent the given conditins.
One is:
Let N = the initial number of contributors and d = the initial donations.
Then, Nd = 2040 and N(d - 23) + =69(d - 23) = 2040.
Substituting and simplifying yields d = 23 + N/3.
N must be divisible by 3.
N......3...6...9.......--->
d.....24...25..26......---> Answer
Nd....72..150..234....---->
To solve for the number of members originally and the amount they donated, we can use the two equations provided:
1. n * d = 2040
2. (n + 69)(d - 23) = 2040
Let's solve these equations step by step.
From the first equation, n * d = 2040, we can determine that the product of the number of members and their donations equal $2040. However, this equation alone cannot give us the specific values for n and d.
To solve for n and d, we need to use the second equation, (n + 69)(d - 23) = 2040. This equation tells us that if there were 69 more people contributing, and each person's donation was $23 less, the total amount raised would still be $2040.
We can simplify the second equation by expanding it:
n * d - 23n + 69d - 69 * 23 = 2040
Rearranging terms and combining like terms:
n * d + 69d - 23n - 69 * 23 = 2040
Combining the terms on the left-hand side:
(n * d - 23n) + (69d - 69 * 23) = 2040
Factoring out n from the first set of terms and 69 from the second set of terms:
n(d - 23) + 69(d - 23) = 2040
Now, we see that we have a common factor of (d - 23) in both terms. We can simplify further:
(n + 69)(d - 23) = 2040
Comparing this equation to the second provided equation, we can see that they are identical. This means that we have the same equation presented in two different ways.
Since we have the same equation twice, we can conclude that there are infinitely many solutions for n and d that satisfy both equations.
However, in order to find a specific solution, we would need either more information or additional equations. The current information provided is insufficient to determine a unique solution for the number of members originally and the amount they donated.
As a result, we cannot determine the specific values for n and d based on the given information.