SOLUTION: Separate 800 into three parts, such that the sum of the first, 1/2 of the second, and 2/5 of the third is 400; and the sum of the second, 3/4 of the first, and 1/4 of the third is

Question 25001: Separate 800 into three parts, such that the sum of the first, 1/2 of the second, and 2/5 of the third is 400; and the sum of the second, 3/4 of the first, and 1/4 of the third is 400.
Answer by quentin252(19) (Show Source): You can put this solution on YOUR website!
alright...
3 equations , 3 variables
1. x+y+z=800
2. x+(1/2)y+(2/5)z=400
3. y+(3/4)x+(1/4)z=400
1. x=800-y-z
2. (800-y-z)+(1/2)y+(2/5)z=400
-> 400 - (1/2)y - (3/5)z = 0
-> y = (400 -(3/5)z)*2 = 800 - (6/5)z
3. (800 - (6/5)z) + (3/4)(800-(800-(6/5)z)-z)) + (1/4)z = 400
-> 800 - (6/5)z + (3/4)(800-800+(6/5)z-z)+(1/4)z = 400
-> 400 - (6/5)z + (3/4)(1/5)z + (1/4)z = 0
-> 400 + (-6/5 + 3/20 + 1/4)z = 0
=> 400 -(4/5)z = 0 -->> (4/5)z = 400 -->> z = 400*5/4 = 500
-> so y = 200 and so x = 100
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