Work out the no of glow in the dark stickers

Question

Emma buys a pack of 221 stickers. The ratio of furry to shiny stickers is 3:5, there are 32 fewer glow in the dark stickers than furry stickers. How many glow in the dark stickers are there?

Answer 1

Victoria, it’s always good to name all the quantities:

Let f = number of furry stickers

Let g = number of glow in the dark stickers

Let s = number of shiny stickers

Now translate the sentences into math

f + s + g = 221

f/s = 3/5

g = f-32

Finally, solve these three equations for these three quantities.

Let’s start by substituting (f-32) for each occurrence of g

f + s + (f-32) = 221 = 2f + s - 32

Next, manipulate f/s = 3/5 to solve for f, by multiplying both sides by s

f = 3s/5

and substitute that into the latest 221 formula

221 = 2(3s/5) + s -32

and solve for s

253 = 6s/5 + s = (6s + 5s)/5 = 11s/5

divide by 11

23 = s/5

multiply by 5

s = 115

now substitute that back in to discover f and g

since

f = 3s/5

f = 3*115/5 = 3*23 = 69

then since they all add up to 221

f + s + g = 221 = 69 + 115 + g = 221

184 + g = 221

g = 221-184 = 37

Answer 2

221/8=27.625

3:5=82.875:138.125

or:

x+(x-32)=221

2x-32=221

2x=253

x=126.5

x-32=94.5