jelly bean problem

Hello, I am stuck again on an extra credit problem. Any hints would be appreciated. A jar contains some red and some yellow jelly beans. If a child ate 1 red jelly bean, 1/7 of the remaining candies would be red. If instead the child ate 5 yellow jelly beans, 1/6 of the remaining candies would be red. How many jelly beans are in the jar? All I have so far is r-1=1/7T, r+y=T, Y-5=1/6T=r. There just seems to be many unknown variables. Thanks

I am stuck again on an extra credit problem. Any hints would be appreciated. A jar contains some red and some yellow jelly beans. If a child ate 1 red jelly bean, 1/7 of the remaining candies would be red. If instead the child ate 5 yellow jelly beans, 1/6 of the remaining candies would be red. How many jelly beans are in the jar? All I have so far is r-1=1/7T, r+y=T, Y-5=1/6T=r. There just seems to be many unknown variables.

With R and Y being the individual quantities:

(R - 1)/(R - 1 + Y) = 1/7 and
R/(R + Y - 5) = 1/6

Two equations, two unknowns.

Go get 'em.

Hello, Thank you for the head start. I was able to work the problem out ,but I am not sure of the reason of the first proportion and why is it equal to 1/7. Thank you

irene12 said:

Hello, Thank you for the head start. I was able to work the problem out ,but I am not sure of the reason of the first proportion and why is it equal to 1/7. Thank you

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A jar contains some red and some yellow jelly beans. If a child ate 1 red jelly bean, 1/7 of the remaining candies would be red. If instead the child ate 5 yellow jelly beans, 1/6 of the remaining candies would be red. How many jelly beans are in the jar?

1/7 of the remaining candies would be red.

after eating one red candy - # of red candies (remaining) = R - 1

after eating one red candy - # of total candies (remaining) = (R + Y) - 1

Thus

\(\displaystyle \frac{R - 1}{R + Y - 1} \ = \ \frac{1}{7}\)