posted by Desperate Please Help .
Please break down and explain answer.
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
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
check: x/2 + x/8 + 9x/32 + 3x/32 = x(1/2 + 1/8 + 9/32 + 3/32)
= x(32/32) = x