Please break down and explain answer.
Thank you:
You make a bag of candy for yourself before you go to the movies. The bag consists of many different pieces of candy with Skittles, M&Ms, Life Savers, and Sour Patch Kids. Half of your pieces of candy are Skittles. A fourth of the remaining pieces of candy is M&Ms. Three-fourths of what is left after the Skittles and M&Ms is Life Savers. The remaining pieces of candy are Sour Patch Kids. What percent of the total pieces of candy are Sour Patch Kids?
1 - 1/2 -(1/2*1/4) - (1/2*1/4*3/4) = ?
Convert answer to percentage.
To find the percentage of the total pieces of candy that are Sour Patch Kids, we need to break down the information provided. Let's go step by step:
1. The bag consists of many different pieces of candy with Skittles, M&Ms, Life Savers, and Sour Patch Kids.
2. Half of your pieces of candy are Skittles. So, let's assume you have X total pieces of candy. Half of them are Skittles, which means you have X/2 Skittles.
3. A fourth of the remaining pieces of candy is M&Ms. After taking half of the candy as Skittles, we have (X - X/2) remaining pieces of candy. Now, divide this by 4 to find the number of M&Ms. This means you have (X - X/2)/4 M&Ms.
4. Three-fourths of what is left after the Skittles and M&Ms is Life Savers. Subtract the number of Skittles and M&Ms from the total number of pieces of candy, which gives us X - X/2 - (X - X/2)/4. Multiply this by 3/4 to find the number of Life Savers, which is (3/4) * (X - X/2 - (X - X/2)/4).
5. The remaining pieces of candy are Sour Patch Kids. Subtract the number of Skittles, M&Ms, and Life Savers from the total number of pieces of candy to find the number of Sour Patch Kids, which is X - X/2 - (X - X/2)/4 - (3/4) * (X - X/2 - (X - X/2)/4).
6. Finally, to find the percentage of the total pieces of candy that are Sour Patch Kids, divide the number of Sour Patch Kids by the total number of pieces of candy (X) and multiply by 100.
So, the equation to find the percentage of the total pieces of candy that are Sour Patch Kids is:
[(X - X/2 - (X - X/2)/4 - (3/4) * (X - X/2 - (X - X/2)/4))/X] * 100.
Simplifying and solving the equation will give you the final answer as a percentage.