pharmaceutical company managed to mix together two kinds of capsules. Each red c

Question

pharmaceutical company managed to mix together two kinds of capsules. Each red capsule weighs 5.00 grains and each green capsule weighs 8.00 grains. 1lb = 7000 grains 453.6 grains (g) Random sampling determined that in every 8000 capsules there are 4850 red capsules, Calculate the percent abundance of red and green capsules in the mix. Calculate the (weighted) average mass (in grains) of a capsule. (average mass times no. of capsules = total mass). Calculate the total number of capsules in 19.00 lb of the mixture. Calculate the number of red capsules in 21.00 kg of mixture Calculate the number of red capsules in 28.0 lb of a mixture having 84.00% red capsules. Hint: calculate a new average mass.

Explanation / Answer

a)

given there are 8000 capsules

and

4850 red capsules

total capsules = red capsules + green capsules

so

8000 = 4850 + green capsules

green capsules = 3150

now

percent abundance of red = ( red capsules / total capsules ) x100

perecent abundance of red = ( 4850/8000) x 100

percent abundance of red = 60.625

percent abundance of green = ( 3150/8000) x 100

percent abundance of green = 39.375

b)

now

total mass = mass of red capsules + mass of green capsules

aslo

mass of red capsules = number of red capsules x mass of each red capsule = 4850 x 5 = 24250

mass of green capsules = number of green capsules x mass of each green capsule = 3150 x 8 = 25200

now

total mass = 24250 + 25200

total mass = 49450 grains

now

avergae mass = total mass / number of capsules

average mass = 49450 / 8000

average mass = 6.18125

so

average mass of a capsule is 6.18125 grains

c) now given

mass of mixture = 19 lb

but

1 lb = 7000 grains

so

mass of mixture = 19 x 7000

mass of mixture = 133000

now

number of capsules = mass of mixture / average mass of capsule

so

number of capsules = 133000/ 6.18125

number of capsules = 21517

so

there are 21517 capsules in the mixture

d)

mass of mixture = 21 kg

= 21 x 1000 g

= 21 x 1000 x (1/453.6) lb

= 21 x 1000 x (1/453.6) x 7000 grain

= 324074 grain

mass of mixture = 324074 grain

number of capsules = 324074 / 6.18125

number of capsules = 52429

now

number of red capsules = total capsules x percent abundance

number of red capsule s= 52429 x 60.625/100

number of red capsules = 31785

so

there are 31785 red capsules in 21 kg of mixture

e)

let the number of red capsules be y

now

percent abundance = ( red capsules / total capsules ) x 100

84 = y x 100 / total capsules

total capsules = 1.19 y

so

green capsules = 1.19 y - y

green capsules = 0.19 y

mass of green capsules = 0.19 y x 8

mass of green capsules = 1.52y

mass of red capsules = y x 5

mass of red capsules = 5y

now

total mass = 5y + 1.52 y

total mass = 6.52y

given

total mass = 28 lb

total mass = 28 x7000 grain

total mass = 196000 grain

so

196000 = 6.52 y

y = 30062

so

there are 30062 red capsules

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