Alex has a number of jelly beans and ate 2/5 of them. Martha found the remaining jelly beans and ate 2/3 of what was left . There are now 51 left. what fraction of the original number of jelly beans did Martha eat? Express your answer as a simplified fraction.
2/3 * 3/5 = 2/5
Alex has X jelly beans.
x - 2x/5 = 3x/5 remaining.
1/3 * 3x/5 = 3x/15 = x/5 remaining.
x/5 = 51.
X = 255.
Martha ate 2/3 * 3x/5 = 2/3 * (3*255)/5 = 102 Jelly beans.
102/255 = 34/85 = 2/5 of original jelly beans.
To find the fraction of the original number of jelly beans that Martha ate, we need to work backwards from the information given.
Let's define the original number of jelly beans as "x."
Alex ate 2/5 of the jelly beans, leaving (1 - 2/5) or 3/5 of the jelly beans. So, there were (3/5)x jelly beans left.
Martha then ate 2/3 of what was left. This means that she ate (2/3) * (3/5)x = (2/5)x jelly beans.
We know that after Martha ate, there were 51 jelly beans left. So we can set up the equation:
(3/5)x - (2/5)x = 51
To solve for x, let's combine like terms:
(1/5)x = 51
To isolate x, multiply both sides of the equation by 5/1:
x = 51 * 5/1
x = 255/1
x = 255
Therefore, the original number of jelly beans was 255.
Now, let's find the fraction of the original number that Martha ate:
Martha ate (2/5)x = (2/5) * 255 = 510/5 = 102
So, Martha ate 102 jelly beans out of the original 255.
To express this as a simplified fraction, we can write:
Martha ate 102/255 of the original number of jelly beans.
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 51.
So, the simplified fraction is:
Martha ate 2/5 of the original number of jelly beans.