Question

Generic sugar which costs $2.23/kg is made by combining brand X sugar which costs $1.18/kg with brand Y sugar which costs $3.98/kg. Find the number of kg of brand X sugar and brand Y sugar required to make 40 kg of generic sugar.

Answer 1

X = 14 kg

Y= 7 kg

Explanation:

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)

------------------

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