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 brans were orginally i

Algebra ->  Percentage-and-ratio-word-problems -> 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 brans were orginally i      Log On


   

Question 990125: 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 brans were orginally in the dish?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The ratio of red jelly beans r to yellow jelly beans y in a dish is 3%3A4.
r%2Fy=3%2F4....solve for r
r=3y%2F4
If Greg eats 3 red jelly beans and 6 yellow ones,the ratio is 4%3A5.
%28r-3%29%2F%28y-6%29=4%2F5.......substitute 3y%2F4 for r
%283y%2F4-3%29%2F%28y-6%29=4%2F5.....cross multiply
5%283y%2F4-3%29=4%28y-6%29
15y%2F4-15=4y-24
15y%2F4-4y=15-24
15y%2F4-16y%2F4=15-24
-y%2F4=-9
-y=-9%2A4
-y=+-36
highlight%28y=+36%29=>yellow jelly beans were originally in the dish
go to r=3y%2F4, substitute 36 for y
r=%283%2A36%29%2F4
r=%283%2Across%2836%299%29%2Fcross%284%291
r=3%2A9
highlight%28r=27%29=> red jelly beans were originally in the dish
check:
r%2Fy=3%2F4
27%2F36=3%2F4
27%2A4=3%2A36
108=108


%28r-3%29%2F%28y-6%29=4%2F5
%2827-3%29%2F%2836-6%29=4%2F5
24%2F30=4%2F5
24%2A5=4%2A30
120=120

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

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 brans were orginally in the dish?
Let multiplicative factor be x

Then he had: 3x red, and 4x yellow, originally

We then get: %283x+-+3%29%2F%284x+-+6%29+=+4%2F5

4(4x - 6) = 5(3x - 3) ------- Cross-multiplying

 16x - 24 = 15x - 15

16x - 15x = - 15 + 24

x, or multiplicative factor = 9



Original number of yellow: 4(9), or highlight_green%2836%29