Question

LaDonna has a banana. She eats 3/5 of it and then gives the rest to her younger brother, Hector. Hector eats 3/5 of what he was given and then gives the rest to his baby sister, Yolanda. Yolanda eats half of what she was given then throws the rest away. What "percentage" of the banana was thrown away? SHOW WORK

Answer 1

So start with the first step, how much did LaDonna eat? 3/5. So...\[1 - \frac{ 3 }{ 5 } = \frac{ 2 }{ 5 }\]
Next, we want to find out how much Hector ate if he ate 3/5 of that. So first, we find 3/5 of 2/5 like so...\[\frac{ 2 }{ 5 } \times \frac{ 3 }{ 5 } = \frac{ 6 }{ 25 }\]
So now we now Hector ate 6/25 of the banana. Now we subtract that from 2/5. But first we make a common denominator, since 5 goes into 25 we change 2/5 into 10/25 like this...\[\frac{ 2 }{ 5 } \times \frac{ 5 }{ 5 } = \frac{ 10 }{ 25 }\]
Since we only multiplied it by one (5/5 = 1) we didn't change the equation. Now, we subtract.\[\frac{ 10 }{ 25 } - \frac{ 6 }{ 25 } = \frac{ 4 }{ 25 }\]
Now, since 4/25 can't be reduced we move on to the last step, Yolando eating half of that piece. So, first we find of of 4/25 by multiplying it by half (1/2)\[\frac{ 4 }{ 25 } \times \frac{ 1 }{ 2 } = \frac{ 4 }{ 50 }\]
So we now know Yolanda ate 4/50 of it, and we subtract that from our 4/25 by finding a common denominator, just like before...\[\frac{ 4 }{ 25 } \times \frac{ 2 }{ 2 } = \frac{ 8 }{ 50 }\]
Now, we subtract...\[\frac{ 8 }{ 50 } - \frac{ 4 }{ 50 } = \frac{ 4 }{ 50 }\]
And for our final answer, we reduce the fraction. Since 2 is the greatest common factor (GCF) of 4/50 we find our final fraction to be 2/25.
But, the question what's that in percentage, so it's not our final answer. The easy way to find a percentage it to get a number is to have something like this ?/100. Because that denominator is 100 the numerator will be your percent. Since our fraction has the denominator of 25 this will be easy, just do the following step:\[\frac{ 2 }{ 25 } \times \frac{ 4 }{ 4 } = \frac{ 8 }{ 100 }\]
There, now since our denominator is 100, we know the numerator is our percent. So our final answer is 8%. 8% was thrown away. If you have any question feel free to message me!
Hope this helps(:

Answer 2

Thank you so much for explaining this to me! I have been stuck on this problem forever.

Answer 3

My pleasure ^.^