Hi All,
We're told that the total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. We're asked for the price of the 5 pounds of regular coffee. The information in the first sentence can be used to create a 2 variable equation, which should get us thinking about 'System math' (re: 2 variables and 2 unique equations):
5(R) + 3(D) = $21.50
R represents the price of a pound of regular coffee while D represents the price of a pound of decaffeinated coffee. If we enough information to create a second, unique equation using those 2 variables, then we can stop working - that information would be enough for us to get to the correct answer and solve for the prices/pound of the two coffees.
(1) If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45.
The information in Fact 1 can be used to create another equation:
5(.9R) + 3(.8D) = $18.45
While the two equations might look a bit 'ugly', it's still a System of equations, so we CAN solve for the two variables. Thankfully, we don't actually have to do that work to know that we COULD, so we would know the exact value of 5R.
Fact 1 is SUFFICIENT
(2) The price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.
With the information in Fact 2, we can create an equation relating the values of 5R and 3D:
5R = 3D + $3.50
Again, we end up with a System of equations, so we CAN solve for the two variables. Thankfully, we don't actually have to do that work to know that we COULD, so we would know the exact value of 5R.
Fact 2 is SUFFICIENT
Final Answer:
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Rich
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