the manager of a store selling tea plans to mix a more expensive tea that costs $6 per pound with a less expensive tea that costs $4 per pound to create a 80-pound blend that will sell for $5.40 per pound. how many pounds of each type of tea are required?
To start this problem you want to start by writing two equations. For this we will draw information from the word problem. Let's call the expensive tea a and the cheaper tea b. We know how much each costs per pound and the total cost that you want. You also need to recognize that the final cost is given per pound. We need to know total cost to get this multiply by the total weight.
6a + 4 b = 5.4 * 80
6a + 4b = 432
You also know the total weight that you want to be 80 pounds.
a + b = 80
Now we want to solve the system of equations. This can be done several ways. I will solve using substitution.
For this solve the second equation for a
a = 80 - b
and then substitute that into the first equation for a.
6(80 - b) + 4b = 432
480 - 6b + 4b = 432
480 - 2b = 432
-2b = -48
b = 24 lbs
The last step will be to solve for a.
a = 80 - 24
a = 56 lbs
To make the desired mix, 56 lbs of the expensive tea and 24 pounds of the cheaper tea should be used.
If you have any questions about what I have done, please ask.
May 18th, 2015
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