Question 1033759: A printing facility prints and packages baseball cards. In April, they package the cards
so that each pack has 20% star players and 80% journeymen. In May, each pack contains
35% star players. A national retailer places an order for 10,000 packs, and wants them to
average 26% star players. How many packs from each month should the printing
facility include?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! order for 10,000 packs.
some packs will have 20% star players.
some packs will have 35% star players.
average for the 10,000 packs needs to be 26% star players.
each pack will have 20% or 35%.
the overall average of star players has to be 26% star players.
this means that the order of 10,000 players has to contain 2600 star players.
let x equal the number of 20% packs.
let y equal the number of 35% packs.
x + y = 10,000
this tells you that the order must contain 10,000 packs, of which x will be packs with 20% players and y will be packs with 35% players.
.20x + .35y = 2600
this tells you that when you add the number of star players from the 20% packs and the number of star players from the 35% packs, the total number of star players has to be 2600, because 2600 is 26% of 10,000.
the equations that need to be solved simultaneously are:
x + y = 10,000
.20x + .35y = 2600
multiply the both sides of the second equation by 5 and leave the first equation as is to get:
x + y = 10,000
x + 1.75y = 13,000
subtract the first equation from the second equation to get:
.75y = 3,000
divide both sides of that equation by .75 to get:
y = 4000.
since y = 4000, x has to be 6000, because x + y = 10,000.
you have x = 6000 and y = 4000.
x + y = 10,000 is ok.
.20x + .35y = .20*6000 + .35*4000 = 1200 + 1400 = 2600 is ok.
number of packs with 20% star players is 6000.
number of packs with 35% star players is 4000.
the total number of star players is .2*6000 + .35*4000 = 2600.
2600 is 26% of 10,000.
everything looks good.
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