In a community,men contribute p each and women q each toward the community development fund.in a week ,3men and 5 women contribute a total of 9,500.00.in another week,5men and 10 women contributed a total of 17,500.
Find the;1. valve of p and q
2.total amount that will be contributed by 8men and 12women
3p+5q = 9500
5p+10q = 17500
Replace with
3p+5q = 9500
p+2q = 3500
Now it's easy to get q:
3(3500-2q)+5q = 9500
q = 1000
so now you can find p and finish it off
To find the values of p and q, we can solve a system of equations based on the given information.
Let's set up the equations:
Equation 1: 3p + 5q = 9,500
Equation 2: 5p + 10q = 17,500
1. To solve for p and q, we can use the method of substitution or elimination. Let's use the method of substitution:
From Equation 1, we can rewrite it as p = (9,500 - 5q)/3.
Substituting this expression for p into Equation 2, we get:
5(9,500 -5q)/3 + 10q = 17,500.
Now we can solve this equation for q:
(47,500 - 25q)/3 + 10q = 17,500.
Let's simplify the equation:
47,500 - 25q + 30q = 52,500.
-25q + 30q = 52,500 - 47,500.
5q = 5,000.
q = 5,000/5.
q = 1,000.
Now, substitute the value of q back into Equation 1 to find p:
3p + 5(1,000) = 9,500.
3p + 5,000 = 9,500.
3p = 9,500 - 5,000.
3p = 4,500.
p = 4,500/3.
p = 1,500.
So, the value of p is 1,500 and the value of q is 1,000.
2. To find the total amount contributed by 8 men and 12 women, we can calculate the total contributions of 8 men and 12 women separately and then add them together.
Total contribution of 8 men: 8p = 8 * 1,500 = 12,000.
Total contribution of 12 women: 12q = 12 * 1,000 = 12,000.
Therefore, the total amount contributed by 8 men and 12 women is 12,000 + 12,000 = 24,000.
To find the values of p and q, we can set up a system of equations using the given information.
Let's define the variables:
p = amount contributed by each man
q = amount contributed by each woman
We know that in the first week, 3 men and 5 women contribute a total of 9,500.
So, we can write the equation:
3p + 5q = 9,500 ...(1)
In the second week, 5 men and 10 women contribute a total of 17,500.
So, we can write the equation:
5p + 10q = 17,500 ...(2)
Now, we can solve this system of equations.
To make the calculations easier, let's divide the equation (2) by 5:
p + 2q = 3,500 ...(3)
We can rewrite equation (3) as:
p = 3,500 - 2q ...(4)
Substituting equation (4) into equation (1), we have:
3(3,500 - 2q) + 5q = 9,500
Simplifying the equation, we get:
10,500 - 6q + 5q = 9,500
Combining like terms, we have:
10,500 - q = 9,500
Bringing the constants to one side, we get:
q = 10,500 - 9,500
q = 1,000
Now, substitute the value of q into equation (4) to find p:
p = 3,500 - 2(1,000)
p = 3,500 - 2,000
p = 1,500
So, the values of p and q are:
p = 1,500
q = 1,000
Now, let's find the total amount contributed by 8 men and 12 women.
Using the values we found,
Total amount contributed by 8 men = 8p = 8 * 1,500 = 12,000
Total amount contributed by 12 women = 12q = 12 * 1,000 = 12,000
Therefore, the total amount contributed by 8 men and 12 women is 12,000 + 12,000 = 24,000.