SOLUTION: The ratio fo 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 jelly beans were originally in t

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio fo 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 jelly beans were originally in t      Log On


   

Question 773272: The ratio fo 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 jelly beans were originally in the dish?
3/4 = RJB/YJB
4rjb = 3yjb
4(rjb-3) = 3(yjb-6)
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
You are asking if you are solving correctly.
Let r = how many red jelly beans
let y = how many yellow jelly beans

Originally, r%2Fy=3%2F4

Ate 3 red beans so now r-3 red beans in the dish;
Ate 6 yellow beans, so y-6 yellow beans still in the jar.
%28r-3%29%2F%28y-6%29=4%2F5

Two equations in the two unknowns r and y.
ORIGINAL EQUATION
4r=3y
4r-3y=0
EATEN EQUATION
4%28y-6%29=5%28r-3%29
4y-24=5r-15
4y-25%2B15=5r
4y-10=5r
5r-4y=-10
SYSTEM TO SOLVE MAY BE:
highlight%285r-4y=-10%29 and highlight%284r-3y=0%29
Multiply by 3 for eaten equation, multiply by 4 for original equation
in these forms, and obtain,...
15r-12y=-30 and 16r-12y=0.
Subtracting the "0" equation from the "-30" equation, obtain:
-1%2Ar=-30
highlight%28r=30%29 and then this means y=r%284%2F3%29 from original ratio, y=30%284%2F3%29=highlight%2840%29
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Originally 30 red jelly beans and 40 yellow jelly beans
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