10 boys and 12 girls collected donation for a project the total amount collected by boys was 600 greater than that of the girls if they average collected of boys was 100 greater than the average collected of the girls how much was collected by the group
Let's represent the amount collected by boys as B and the amount collected by girls as G.
From the problem, we have two equations:
1) B = G + 600 (the total amount collected by boys was 600 greater than that of the girls)
2) B/10 = G/12 + 100 (the average collected by boys was 100 greater than the average collected by the girls)
We can multiply equation 2 by 10 and equation 1 by 12 to eliminate the denominators:
10B = 12G + 1200 (multiplied equation 2 by 10)
12B = 12G + 7200 (multiplied equation 1 by 12)
Subtracting the equations, we get:
12B - 10B = 7200 - 1200
2B = 6000
B = 3000
Substituting B = 3000 into equation 1, we have:
3000 = G + 600
G = 2400
Therefore, the total amount collected by the group is:
B + G = 3000 + 2400 = <<3000+2400=5400>>5400
So, the group collected $5400.