April 17, 2011

Green tea word problem

Photo credit: leojmelsrub

Ahmed sent me in this kind of word problem:


A tea producer want to market mixed green tea leaves at $14 per pound. how many pounds of high mountain green tea leaves worth $20 per pound must be mixed with 90 pounds of regular green tea leaved worth $10 per pound?

I have solve many problems like this one on my blog, but it never hurts to solve some more. This can be solved with algebra, using a chart. I've done that before for similar problems... so if you are reading this, and you feel a bit "rusty" in this area, try to make the chart yourself first, before you read further!

For the chart, we also need to choose a variable or several. In this case it is easy:  the unknown is obviously what is asked, or the amount of high mountain green tea. Note also that the cost is always the price per pound times the amount.


mountain green   regular green  the mixture
 tea leaves  tea leaves
--------------------------------------------------------------------------
amount |   x   90   90 + x
--------------------------------------------------------------------------
cost   |  20x   $900   14(90 + x)
--------------------------------------------------------------------------

The chart is ready. Its purpose is to help us write an EQUATION of some sort which will solve x.

So where can we find something equals something? It comes from the cost. The COST of mountain green tea + the COST of regular green tea = COST of the mixture.

20x + 900 = 14(90 + x)

20x + 900 = 1260 + 14x

6x = 360

x = 60 
 
Now, let's check. That's always the last step in solving equations.

We need 60 pounds of mountain green tea leaves mixed with 90 pounds of regular green tea leaves. The mixture will weigh 150 pounds. The cost of mountain green tea leaves will be $1200, the cost of regular green tea will be $900, and the total cost will be $2100. Calculating cost per pound: $2100 / 150 lb = $14 per pound, so it checks.
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