On 01/28/2011 12:33 PM, mathematicsstudent wrote: > Hello, > > I have to solve this problem: > > The manager of a bulk foods establishment sells a trail mix for $8 > per pound and premium cashews for $15 per pound. The manager wishes > to make a 105-pound trail mix-cashew mixture that will sell for $12 > per pound. How many pounds of each should be used? > > I figured out that the first equation should be: X + Y = 105 > > How do I write the other equation? I tried this, but it didn't work: > 08x + .15Y = 12 > > If you can guide me along, I would greatly appreciate it! > > Thank you.
There are a couple of questions that have to be answered. First, is how to express the two variables in terms of a single variable.
Pounds(trailmix) + Pounds(cashews) = 105 Therefore P(cashews) = 105 - P(trailmix) Thus, we have our two variables:
P = pounds of trailmix 105 - P = pounds of cashews
Next we have to determine the weighted average. The basic formula would be Average price = $/pounds.
Using dimensional analysis, we can arrive at the weighted average as follows:
Average Price = ($/lb) / Total Pounds
This is because the 'pounds' cancel each other out, and you are left with price.