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 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were originally in the dish?

Answer 1

x - the number of red jelly beans
y - the number of yellow jelly beans

The ratio of red jelly beans to yellow jelly beans is 3:4.

`(x)/(y)=(3)/(4) \ \ \ |* y \\ x=(3)/(4)y`

If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5.

`(x-3)/(y-6)=(4)/(5) \ \ \ |\hbox{cross multiply} \\ 5(x-3)=4(y-6) \\ 5x-15=4y-24 \ \ \ |+15 \\ 5x=4y-9 \ \ \ |/ 5 \\ x=(4)/(5)y-(9)/(5)`


`x=x \\ (3)/(4)y=(4)/(5)y-(9)/(5) \\ (3)/(4)y-(4)/(5)y=-(9)/(5) \\ (15)/(20)y-(16)/(20)y=-(9)/(5) \\ -(1)/(20)y=-(9)/(5) \ \ \ |* (-20) \\ y=-(9)/(5) * (-20) \\ y=9 * 4 \\ y=36`

There were 36 yellow jelly beans in the dish.