The ratio of red jelly beans to yellow jelly beans in a dish is 2:3. If I eat 3 red jelly beans and 6 yellow ones the ratos is 4:5. How many yellow jelly beans were orginally in the dish?
r/y = 2/3
(r-3)/(y-6) = 4/5
r=9 y=13.5
?? is there a typo somewhere?
No, there is no typo. This is how it was written in the textbook. Thanks for the help. We have been working on this problem for days.
On our worksheet this is the same question, but ours states the original ratio of red to yellow as 3:4.
To answer this question, we can use a system of equations. Let's assign variables to the unknown quantities.
Let's say the initial number of red jelly beans is 2x, and the initial number of yellow jelly beans is 3x.
According to the given information, the ratio of red jelly beans to yellow jelly beans is 2:3, so we have the equation:
(2x)/(3x) = 2/3
Now, let's calculate the remaining number of jelly beans after eating 3 red jelly beans and 6 yellow jelly beans.
After eating 3 red jelly beans, we are left with 2x - 3.
After eating 6 yellow jelly beans, we are left with 3x - 6.
According to the updated ratio, (2x - 3)/(3x - 6) = 4/5.
Now, we can solve this system of equations:
(2x)/(3x) = 2/3 ------(1)
(2x - 3)/(3x - 6) = 4/5 ------(2)
To eliminate the denominators, we can cross-multiply:
(2x)(3) = (2)(3x)
6x = 6x
(2x - 3)(5) = (4)(3x - 6)
10x - 15 = 12x - 24
Rearranging the second equation, we get:
2x = 9
x = 9/2
x = 4.5
Now, we can substitute the value of x back into the initial number of yellow jelly beans:
3x = 3(4.5) = 13.5
Therefore, there were originally 13.5 yellow jelly beans in the dish. Since we can't have a fraction of a jelly bean, we can round down to the nearest whole number.
So, there were originally 13 yellow jelly beans in the dish.