SOLUTION: The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were in the d

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Question 1033571: The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were in the dish?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the original number of red DISABLED_event_ones= +r+
Let the original number of yellow DISABLED_event_ones= +y+
-----------------------------------------
(1) +r%2Fy+=+3%2F4+
(2) +%28+r-3+%29+%2F+%28+y+-+6+%29+=+4%2F5+
--------------------------
(1) +r+=+%283%2F4%29%2Ay+
and
(2) +r+-+3+=+%284%2F5%29%2A%28+y+-+6+%29+
Substitute (1) into (2)
(2) +%283%2F4%29%2Ay+-+3+=+%284%2F5%29%2A%28+y+-+6+%29+
Multiply both sides by +20+
(2) +15y+-+60+=+16%2A%28+y+-+6+%29+
(2) +15y+-+60+=+16y+-+96+
(2) +y+=+36+
and
(1) +r+=+%283%2F4%29%2Ay+
(1) +r+=+%283%2F4%29%2A36+
(1) +r+=+27+
----------------------
36 yellow beans were in the dish
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check:
(1) +r%2Fy+=+3%2F4+
(1) +27%2F36+=+3%2F4+
(1) +%28+9%2F9+%29%2A%28+3%2F4+%29+=+3%2F4+
(1) +3%2F4+=+3%2F4+
and
(2) +%28+r-3+%29+%2F+%28+y+-+6+%29+=+4%2F5+
(2) +%28+27-3+%29+%2F+%28+36+-+6+%29+=+4%2F5+
(2) +24+%2F+30+=+4%2F5+
(2) +%28+6%2F6+%29%2A%28+4%2F5+%29+=+4%2F5+
(2) +4%2F5+=+4%2F5+
OK