SOLUTION: There were 360 red and blue marbles in a bag at first. 25% of the number of red marbles and 40% of the number of blue marbles were added. In the end, there were 471 marbles in the

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: There were 360 red and blue marbles in a bag at first. 25% of the number of red marbles and 40% of the number of blue marbles were added. In the end, there were 471 marbles in the       Log On


   

Question 1204320: There were 360 red and blue marbles in a bag at first. 25% of the number of red marbles and 40% of the number of blue marbles were added. In the end, there were 471 marbles in the bag altogether.
How many blue marbles were in the bag at first?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

b = number of blue marbles at first
360-b = number of red marbles at first
b > 0 and b is an integer

40% of b = 0.40b = number of blue marbles added
b+0.40b = 1.40b = total number of blue marbles after adding those extra

1.25(360-b) = total number of red marbles after extra reds are added in


1.40b + 1.25(360-b) = 471
1.40b + 450-1.25b = 471
0.15b + 450 = 471
0.15b = 471 - 450
0.15b = 21
b = 21/0.15
b = 140
360-b = 360-140 = 220

At first there are 140 blue marbles and 220 red marbles.

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Check:

25% of red = 0.25*220 = 55 extra red added
40% of blue = 0.40*140 = 56 extra blue added

55+56 = 111 extra marbles added
360+111 = 471 which confirms the answer is correct.


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Answer: There are 140 blue marbles to start with.