A mixture of 30 pounds of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90 cents a pound. How many pounds of the $1.50 chocolate were used to make the mixture?
10 lbs of the more expensive chocolate was used.
Based on total pounds we know:
Based on cost we know
We can simplify the cost equation:
move everything to one side:
Now we can solve the system:
From the first equation we know that
subtract 12 from both sides:
divide through by
This is a simultaneous equation problem.
Chocolate used at $1.50 per pound is 10 pounds
Chocolate used at $0.90 per pound is 20 pounds
Let the weight of chocolates worth $0.90 a pound be
Let the weight of chocolates worth $1.50 a pound be
The value of the blend is
Thus we have:
You may choose which one you so wish to substitute for. I choose
Dropping the units of measerment for now.
Subtract 26 from both sides
Divide both sides by