A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used?
One of the better ways to tackle this problem type is to consider them as a set of fraction that sum to the value of 1. Where 1 represents the whole of the final blend.
Let the proportion of the $0.20 be
Then the proportion of the $0.68 is
Set the target at $0.54
Dropping the unit of measurement ($ ) for now we have
Lets get rid of the decimals for now and multiply everything by 100
So the proportion of the $0.68 is
Method 2 of 2
An amazing approach that is not commonly used. Very fast once used to it.
This uses the principle of a straight line graph.
Let the weight of the $0.20 bean be
Let the weight of the $0.68 bean be
Then by considering only say
So it is possible to determine the part of the answer by considering just
If all the target blend total value is
Plotting this on the graph we have:
The slope of all is the same as the slope of a part of it
So we have: