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?
total = 100
sk = 50 and 50 are left
mm = .25*50 = 12.5 and 37.5 are left
LS = .75*37.5= 28.125 and 9.375 are left
so 9.375 percent are Sour Patch
let the total be x
Skittles = x/2
M&M = (1/4)(x/2) = x/8
accounted for is: x/2 + x/8 = 5x/8
leaving 3x/8
Life Safers = (3/4)(3x/8) = 9x/32
so far accounted for = 5x/8 + 9x/32 = 29x/32
leaving 3x/32 as Sour Patch Kids.
percentage of SPK = (3x/32) / x
= 3/32 = .09375 or
9.375%
check: x/2 + x/8 + 9x/32 + 3x/32 = x(1/2 + 1/8 + 9/32 + 3/32)
= x(32/32) = x
Bn
Hhy
To find the percentage of Sour Patch Kids in the bag of candy, we need to understand the information given step by step.
First, we are told that half of the total pieces of candy are Skittles. So, let's say there are 100 pieces of candy in total. This means that 50 pieces are Skittles.
Next, we are told that a fourth of the remaining pieces of candy is M&Ms. The remaining pieces of candy after the Skittles are 50. So, one-fourth of 50 is 12.5. Since you cannot have a fraction of a candy, this means there are 12 M&Ms.
Now, we need to calculate how many Life Savers we have. We're told that three-fourths of what is left is Life Savers. So, what is left after the Skittles and M&Ms? 50 (total) - 50 (Skittles) - 12 (M&Ms) = 38 pieces.
Three-fourths of 38 is (3/4) * 38 = 28.5. Again, we cannot have a fraction of a candy, so we round down to the nearest whole number. This means we have 28 Life Savers.
Finally, we can find the number of Sour Patch Kids by subtracting the total number of Skittles, M&Ms, and Life Savers from the total number of candies: 100 - 50 (Skittles) - 12 (M&Ms) - 28 (Life Savers) = 10 Sour Patch Kids.
To find the percentage of Sour Patch Kids in the total bag of candy, we divide the number of Sour Patch Kids by the total number of candies and multiply by 100: (10 / 100) * 100 = 10%.
Therefore, 10% of the total pieces of candy are Sour Patch Kids.