Question

Plastic material worth 2.75\kg is to be mixed with plastic worth 3.50\kg to make up a 50 kg mixture to sell at 3 kg.

Answer 1

Let the amount of 1st plastic needed = x kg
Let the amount of 2nd plastic needed = y kg

therefore by data
x+y=50 -1st eq

Therefore also by data,
2.75x+3.5y=3(50)
2.75x +3.5y=150 -2nd eq

Multiply the second equation by 100
275x+350y=15000

Now simplifying this equation we have,
11x + 14y =600 -3rd eq

Multiply the first equation by 11,
11x +11y=550 -4th
Therefore subtracting the 4th eq from the 3rd we have,
3y=50
y=50/3=16.67kg
therefore x=150-50/3=100/3=33.33kg

Hence you need to mix 16.67 kg of the first plastic and 33.33kg of the second plastic !!

Answer 2

3.5k + 2.75 ( 50 -k) = 3 * 50
-> .75k = 150 - 137.5
=> K = 12.5/ .75 = 16.7 kg of $3.5/kg

Answer 3

and 33.3 kgs of $2.5/kg