+129 Ben had some red, blue and yellow cards. He had 156 more blue cards than red cards and 2/3 as many yellow cards as red cards. He gave away 1/3 of his red cards, 5/6 of his blue cards and 50% of his yellow cards. In the end, he had 250 cards left.
(a) How many cards did Ben have at first?
(b) How many blue cards did Ben give away?
Let's assume the number of red cards
Ben had initially is "R,,"child-0-0">
Let's assume the number of red cards Ben had initially is "R," the number of blue cards is "B," and the number of yellow cards is "Y."
According to the given conditions:
Condition (a)
Ben had 156 more blue cards than red cards: B = R + 156
Ben had 2/3 as many yellow cards as red cards: Y = (2/3) * R
Condition (b)
Ben gave away 1/3 of his red cards:
R - 1/3 * R
Ben gave away 5/6 of his blue cards:
B - 5/6B
Ben gave away 50% of his yellow cards:
Y - 1/2Y
Condition (c)
In the end, he had 250 cards left:
(R - 1/3R) + (B - 5/6B) + (Y - 1/2Y) = 250
=> 2/3R + 1/6B + 1/2Y = 250 - - - - (1)
From the above equation (1), we have:
2/3R + 1/6B + 1/2Y = 250
=> 2/3R + 1/6(R + 156) + 1/2(2/3R) = 250
=> 4/6R + 1/6(R +156) + 2/6R = 250
=> 7R/6 + 26 = 250
=> 7R/6 = 250 - 26
=> 7R/6 = 224
=> R = 192
Therefore, the number of red cards= 192 number
Number of Blue cards=192+156=348
Number of yellow cards 2/3*192=128
total Cards=192+348+128=668
Ben gave away 5/6 of blue cards:
5/6B = 5/6 * 348 = 290
Therefore, Ben gave away 290 blue cards
a) Total Cards=192+348+128=668
b) Ben gave away 290 blue cards
