There were some jelly beans in a jar putri ate 1 4 of the jelly beans emma ate 4 9 of the remaining jelly beans there were 35 jelly beans left in the jar how many jelly beans did putri eat?
Let's break down the problem step by step.
Putri ate 1/4 of the jelly beans.
This means there were 3/4 of the jelly beans left in the jar.
Emma then ate 4/9 of the remaining jelly beans.
This means there were (1 - 4/9) = 5/9 of the original jelly beans left in the jar.
We know that 5/9 of the original jelly beans is equal to 35 jelly beans.
So, 1/9 of the original jelly beans is equal to 35/5 = 7 jelly beans.
Therefore, Putri ate 1/4 x 7 = 7/4 = <<1/4*7=1.75>>1.75 jelly beans. Answer: \boxed{1.75}.
To find out how many jelly beans Putri ate, we need to work backwards from the given information.
Let's start with the total number of jelly beans in the jar. We know that there were initially 35 jelly beans left after Emma ate 4/9 of the remaining jelly beans.
Next, we need to determine the number of jelly beans before Emma ate 4/9 of them. To do this, we can multiply the remaining jelly beans by (9/5), which is the reciprocal of 4/9.
So, we have:
35 jelly beans * (9/4) = 78.75 jelly beans
Since we can't have a fraction of a jelly bean, we round the result. Therefore, before Emma ate the jelly beans, there were approximately 79 jelly beans in the jar.
Now, we need to determine the number of jelly beans Putri ate. We know that she ate 1/4 of the jelly beans in the jar. To find out how many jelly beans that is, we multiply the total number of jelly beans by 1/4.
So, we have:
79 jelly beans * (1/4) = 19.75 jelly beans
Again, we round the result to get a whole number. Therefore, Putri ate approximately 20 jelly beans.
Therefore, Putri ate around 20 jelly beans.
To find out how many jelly beans Putri ate, we can follow these steps:
Step 1: Calculate the number of jelly beans remaining after Putri ate.
When Putri ate 1/4 of the jelly beans, she left 3/4 of the beans in the jar.
So, if we let 'x' represent the initial number of jelly beans, the number of jelly beans remaining after Putri's consumption can be expressed as (3/4)x.
Step 2: Calculate the number of jelly beans remaining after Emma ate.
When Emma ate 4/9 of the remaining jelly beans, she left 5/9 of the beans in the jar.
Therefore, the number of jelly beans remaining after Emma's consumption can be expressed as (5/9) * (3/4)x.
We are given that the number of jelly beans remaining in the jar is 35, so we can equate the expression from step 2 to 35 and solve for 'x'.
(5/9) * (3/4)x = 35
Step 3: Solve for 'x'.
To simplify the equation, we can cross-multiply:
(5/9) * (3/4)x = 35
(15/36)x = 35
Next, we can multiply both sides of the equation by 36/15 to isolate 'x':
x = (35 * 36) / 15
Simplifying further:
x = 84
Therefore, the initial number of jelly beans in the jar was 84.
Step 4: Calculate the number of jelly beans Putri ate.
From step 1, we found that the number of jelly beans remaining after Putri's consumption was (3/4)x.
Substituting 'x' with 84:
Number of jelly beans remaining after Putri's consumption = (3/4) * 84 = 63
Step 5: Calculate the number of jelly beans Putri ate.
The number of jelly beans Putri ate can be calculated by subtracting the number of jelly beans remaining after her consumption from the initial number of jelly beans:
Number of jelly beans Putri ate = 84 - 63 = 21
Therefore, Putri ate 21 jelly beans.