Question

Miguels coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $5.95 per pound, and type B coffee costs $4.65 per pound. This months blend used three times as many pounds of type B coffee as type A, for a total cost of $796.00. How many pounds of type A coffee were used?

Answer 1

40 lb of Type A

Explanation:

3 pounds of Type B and 1 pound of Type A will give 4 pounds of mix at a cost of ...

3($4.65) +($5.95) = $19.90

Then $796 is the cost equivalent of 796/19.90 = 40 times that 4-lb mix. Since each instance of that 4-lb mix has 1 lb of Type A, $796 worth of blend has 40 lb of Type A coffee.

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Additional comment

If you'd like to do this using a variable, you can let 'a' represent the amount of Type A coffee used. Then (3a) is the amount of Type B, and the total cost is ...

5.95a +4.65(3a) = 796

19.90a = 796 . . . . . . . . simplify

a = 796/19.90 = 40 . . . as above

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There will be 120 lb of Type B coffee in that amount of blend.