The ratio of red jelly beans to yellow ones is 3:4. If I eat 3 red ones and 6 yellow ones, the ratio is 4:5. How many yellow ones to begin with?
number of reds ---- 3x
number of yellows -- 4x
(3x-3)/(4x-6) = 4/5
16x - 24 = 15x - 15
x = 9
number of reds at the start = 3(9) = 27
number of yellows at the start = 4(9) = 36
check: origianl ratio = 27/36 = 3/4
after "eating" ratio = 24/30 = 4/5
To solve the problem, we can set up a system of equations based on the given information.
Let's assume the initial number of red jelly beans is 3x and the initial number of yellow jelly beans is 4x (as the ratio of red to yellow beans is 3:4).
According to the first statement, if you eat 3 red jelly beans and 6 yellow jelly beans, the new ratio is 4:5. This means the equation becomes:
(3x - 3) : (4x - 6) = 4 : 5
To make it easier to solve, we can cross-multiply:
5(3x - 3) = 4(4x - 6)
Now, let's simplify and solve for x:
15x - 15 = 16x - 24
Move the x terms to one side of the equation and the numbers to the other side:
16x - 15x = -24 + 15
x = 9
So, the initial number of yellow jelly beans is 4x = 4 * 9 = 36 yellow jelly beans. Therefore, there were initially 36 yellow jelly beans.