The ratio of red jellybeans to yellow jellybeans is 3:4. Jerry eats 3 red jellybeans and 6 yellow leaving the remaining ratio of red jellybeans to yellow jellybeans as 4:5. How many yellow jellybeans were originally in the jar?
Let's start by using algebra to solve the problem.
Let's call the original number of red jellybeans "3x" (since the ratio of red to yellow is 3:4, we can think of the total number of jellybeans as 3x + 4x = 7x, where 4x is the number of yellow jellybeans).
After Jerry eats 3 red jellybeans and 6 yellow jellybeans, there are 3x - 3 red jellybeans and 4x - 6 yellow jellybeans left. The new ratio of red to yellow is given as 4:5, so we can set up an equation:
(3x - 3)/(4x - 6) = 4/5
To solve for x, we can cross-multiply and simplify:
5(3x - 3) = 4(4x - 6)
15x - 15 = 16x - 24
x = 9
Now we know that the original number of yellow jellybeans was 4x = 36.
Let's solve this problem step by step.
Step 1: Let's assume the initial number of red jellybeans is represented by "3x" and the initial number of yellow jellybeans is represented by "4x". Since the ratio of red jellybeans to yellow jellybeans is 3:4, we can express this as (3x):(4x).
Step 2: Jerry eats 3 red jellybeans and 6 yellow jellybeans. After Jerry eats, there are (3x-3) red jellybeans and (4x-6) yellow jellybeans left in the jar.
Step 3: The remaining ratio of red jellybeans to yellow jellybeans is given as 4:5. Therefore, we have the equation (3x-3)/(4x-6) = 4/5.
Step 4: Cross-multiplying the equation, we get 5(3x-3) = 4(4x-6).
Step 5: Simplifying the equation, we have 15x - 15 = 16x - 24.
Step 6: Rearranging the equation, we have 16x - 15x = -24 + 15.
Step 7: Simplifying further, we get x = 9.
Step 8: Now, we can find the initial number of yellow jellybeans. Substituting x = 9 into the expression 4x, we get 4(9) = 36.
Therefore, there were originally 36 yellow jellybeans in the jar.