Arabica coffee costs $ 28 per pound and Robusta coffee costs $ 8.75 per pound. How many pounds of arabica coffee must you mix with 3 pounds of Robusta coffee to make a blend that costs $ 15.50 per pound?

The correct answer is: 1.62 pounds of Arabica coffee should be added to the blend.

step-by-step solution:-
Let the quantity of arabica coffee to be mixed be x pounds.
From the given information we get-
Quantity of Robusta coffee to be mixed = 3 pounds
Cost of Arabica coffee = $ 28 per pound
Cost of Robusta coffee = $ 8.75 per pound
Cost of blended coffee = $ 15.5 per pound
Now, we know that-
Total Quantity of blend = Quantity of Arabica coffee + Quantity of Robusta coffee
∴ Total Quantity of blend = x + 3 ................................................................... (Equation i)
Cost of Arabica coffee = Quantity of Arabica coffee × Price per pound
∴ Cost of Arabica coffee = x pounds × $ 28 per pound ................................. (From given information)
∴ Cost of Arabica coffee = $ 28x ......................................................................... (Equation ii)
Cost of Robusta coffee = Quantity of Robusta coffee × Price per pound
∴ Cost of Robusta coffee = 3 pounds × $ 8.75 per pound ................................. (From given information)
∴ Cost of Robusta coffee = $ 26.25 ......................................................................... (Equation iii)
Cost of blended coffee = Quantity of blended coffee × price per pound
∴ Cost of blended coffee = (x + 3) × 15.5 ....................................................... (From given information & Equation i)
∴ Cost of blended coffee = 15.5 × x + 15.5 × 3 ........... [Distributive property- a (m+n) = am + an]
∴ Cost of blended coffee = 15.5x + 46.5 ........................................................ (Equation iv)
Cost of blended coffee = Cost of Arabica coffee + Cost of Robusta coffee
                                                                                         ∴ 15.5x + 46.5 = 28x + 26.25 ................................................ (From Equations ii, iii & iv)
                                                                                          ∴ 46.5 - 26.25 = 28x - 15.5x ....................................... (Taking all variables & constants                                                                                                                                                                                     on either sides of the equation)
                                                                                                     ∴ 20.25 = 12.5x
                                                                                                    ∴ 20.25/12.5 = x ............................................... (Dividing both sides by 12.5)
                                                                                                         ∴ 1.62 = x
Final Answer:-
∴ 1.62 pounds of Arabica coffee should be added to the blend.