mixture word problem

Question

Generic sugar which costs $2/kg is made by combining brand X sugar which costs $1/kg with brand Y sugar which costs $4/kg. Find the number of kg of brand X and brand Y sugar required to make 21 kg of generic sugar.

Answer 1

LET  X and Y equal the amounts of brand X and Y

 

X = kg of brand X

Y = kg of brand Y 

 

we know:

1)   X    +    Y   =   21    (kg)

 

2)   1X  +   4Y  =   2(X + Y)        (This is the cost/kg * amounts for total cost)  

Coefficients 1,4,2  are the cost/kg)

 

substitute eq. 1 (X+Y), = 21 into right side of equation 2

 

1X + 4Y = (21)*2

 

use elimination to solve 2 equations

 

 X   +   Y = 21

 X   + 4Y = 42        (now subtract,       note:  I wrote the 1X as just X)

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 0     -3Y  = -21       OR   Y = 7 kg   so X = (21-7) OR   X = 14 kg

 

X = 14 kg

Y =  7 kg