Question 1125843: In a collection of black, white and blue marbles, there are 25% more black marbles than white marbles, and there are 40% more blue marbles than black marbles. If C is the number of black marbles, what is the total number of marbles?
Answer by kasperk(4)   (Show Source):
You can put this solution on YOUR website! "25% more" really means 100% + 25% = 125%, so when they say "25% more black marbles than white marbles," it means "Black is 125% of White."
Similarly, "40% more blue marbles than black marbles" means "Blue is 140% of Black."
The question asks to use C to represent the number of black marbles, but I am going to do something that flows better by starting with W for the number of White marbles rather than C for the number of black marbles.
Let W = the number of White marbles
Since "Black is 125% of White," we say Black = 1.25W because 125% in decimal form is 1.25 and the word "of" in math means multiply.
Since "Blue is 140% of Black," Blue = 1.40·Black = 1.40·(1.25W) = 1.75W
So we now have:
W = number of White
1.25W = number of Black
1.75W = number of Blue
But the question asks us to use C for the number of Black marbles. Therefore, equate the above number of Black, 1.25W, with C --> 1.25W = C --> W = 0.8C. Now we can substitute W = 0.8C into the above expressions in terms of W:
W = 0.8C = number of White marbles
1.25W = C = number of Black marbles
1.75W = 1.75(.8C) = 1.4C = number of Blue marbles
If we add up blue + black + white, we have 0.8C + C + 1.4C = 3.2C
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