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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?

 Jul 20, 2023
 #5
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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

 Jul 21, 2023

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