Question

The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and six tallow ones, tie ratio is 4:5. How many yellow jelly beans were originally on the dish?

Answer 1

disclamer: the following is confusing but I will transcribe what is going on in my head

3:4, 3+4=7
4:5, 4+5=9

hm
we can do fractions

3:4, 4 units is yellow
4/7 of all is yellow

4:5, 5/9 of all is yellow

all end is all-9


yellow intial=6+yellowfinal

yellowinitial=(4/7)all
(let's say all=x)
yi=(4/7)x
final=(5/9)(x-9)

yi=6+yf
(4/7)x=6+(5/9)(x-9)
times both sides by  63
36x=378+35(x-9)
distribute
36x=378+35x-315
36x=35x+63
minus 35x both sides
x=63

yellow=(4/7)(x)
yellow=(4/7)(63)
yellow=36


there wer 36 originally

Answer 2

Answer:  The required number of yellow jelly beans is 36.

Step-by-step explanation:  Given that the ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and six yellow ones, the ratio is 4:5.

We are to find the number of jelly beans that were originally on the dish.

Let 3x and 4x represents the number of red jelly beans and yellow jelly beans respectively.

Then, according to the given information, we have

$\dfrac{3x-3}{4x-6}=\dfrac{4}{5}\\\\\\\Rightarrow 15x-15=16x-24\\\\\Rightarrow 16x-15x=24-15\\\\\Rightarrow x=9.$

So, the number of yellow jelly beans is given by

$4\times9=36.$

Thus, the required number of yellow jelly beans is 36.