perplexus.info :: Just Math : Red and Blue chips

Red and Blue chips (Posted on 2024-01-28)

Jane and Fred each have their own collection of red and blue bingo chips. The ratio of the number of Jane’s chips to the number of Fred’s chips is 3:2. When they combine their chips, the ratio of the number of red chips to the number of blue chips is 7:3. For Jane’s chips, the ratio of the number of red chips to the number of blue chips is 4:1.

What is the ratio of the number of red chips to the number of blue chips for Fred’s bingo chips?

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

Comment 3 of 3 |

jr = 4x

jb = x

jr + fr = 7y

jb + fb = 3y

(jr+jb)/(fr+fb) = 3/2

2(jr+jb) = 3(fr+fb)

10 x = 3(7y - jr + 3y - jb)

10x = 30y - 3(jr+jb)

10x = 30y - 15x

30y = 25x

y = (5/6)x

fr = 7y - jr = (35/6)x - 4x = (11/6) x

fb = 3y - jb = (15/6)x - x = (9/6) x

The ratio of Fred's red to blue chips is 11:9

If, for example, x=6, y=5

Red Blue Total

Jane 24 6 30

Fred 11 9 20

total 35 15 50

Posted by Larry on 2024-01-28 16:30:37

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