In a community, men contributed #p each women #q each towards the community development fund. In a week, 3 men and 5 women contributed a total of#9500.00. In another week, 5 men and 10 women contributed a total of #17,500.00. Find the: (I) Value of p and q. (Ii) Total amount that will be contributed by 8 men and 12 women
8p+ 12q=17pq
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To solve this problem, we will set up a system of equations based on the given information.
Let's consider the first week:
We are told that 3 men and 5 women contributed a total of #9500.00. This can be expressed as:
3p + 5q = 9500 ..........(Equation 1)
Now, let's consider the second week:
We are told that 5 men and 10 women contributed a total of #17,500.00. This can be expressed as:
5p + 10q = 17500 ..........(Equation 2)
To find the value of p and q, we can solve this system of equations using any suitable method, such as substitution or elimination.
Let's solve this system of equations using the elimination method:
Multiply equation 1 by 2 and equation 2 by 1, so that the coefficients of p in both equations are the same:
6p + 10q = 19000 ..........(Equation 3)
5p + 10q = 17500 ..........(Equation 2)
Now, subtract Equation 2 from Equation 3:
(6p + 10q) - (5p + 10q) = 19000 - 17500
p = 1500
Substituting the value of p back into Equation 1, we can find q:
3p + 5q = 9500
3(1500) + 5q = 9500
4500 + 5q = 9500
5q = 5000
q = 1000
Therefore, the value of p is #1500 and the value of q is #1000.
Now, let's calculate the total amount that will be contributed by 8 men and 12 women:
Using the values of p and q we just found, we can calculate the contribution of 8 men:
8p = 8 * 1500 = #12,000
And the contribution of 12 women:
12q = 12 * 1000 = #12,000
Finally, the total amount contributed by 8 men and 12 women would be:
Total amount = Contribution of men + Contribution of women
Total amount = #12,000 + #12,000 = #24,000
So, the total amount that will be contributed by 8 men and 12 women is #24,000.
3p + 5q = 9500
5p + 10q = 17500 ----> p + 2q = 3500 ---> p = 3500-2q
sub that into the first:
3(3500-2q) + 5q = 9500
10500 - 6q + 5q = 9500
-q = -1000
q = 1000
go back to p = 3500-2q and find p
at which point you can find 8p + 12q