Treena P.

asked • 01/04/13

algebra help

A distributor needs to mix a 20% fat-content chocolate with a 40% chocolate to create 200 kilograms of a 37% chocolate. How manA candy distributor needs to mix a 20% fat-content chocolate with a 40% fat-content chocolate to create 200 kilograms of a 37% fat-content chocolate. How many kilograms of each kind of chocolate must they use?y kilograms of each kind of chocolate must they use

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Inactive Tutor answered • 01/04/13

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Ok. So our end result is 200 kg of 37% fat chocolate. Therefore, the total mass of fat needed is .37*200=74 kg of fat. 

let a=mass of chocolate with 20% fat. let b=mass of chocolate with 40% fat.

our end product weighs 200 kg, so a+b=200

our end product is 37% fat, so (.2a+.4b)/200=0.37.

we rearrange the first equation a+b=200 to make a=200-b

we can substitute (200-b) for the variable 'a' in the second equation

therefore,

(.2(200-b)+.4b)/200=.37

simplify 

(40-.2b+.4b)/200=.37

simplify

(40+.2b)=74    (74=200*.37)

.2b=34

b=170   

now go back to your original equation:

a=200-b

a=200-170=30

 

you use 170 kg of 40% fat chocolate, and 30 kg of 20% fat chocolate.

 

Please leave a thank you on my tutoring profile!

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