euben's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Reuben $5.70 per pound, and type B coffee costs $4.30 per pound. This month, Reuben made 167 pounds of the blend, for a total cost of $820.30. How many pounds of type A coffee did he use?

Answer:The quantity of type A coffee is 73 poundsThe quantity of type B coffee is 94 pounds . Step-by-step explanation:Given as :The price of Type A coffee costs = $ 5.70 per poundThe price of Type B coffee costs = $ 4.30 per poundThe total quantity of coffee does Reuben purchases = 167 poundsThe total cost of the coffee for 167 pounds = $ 820.30Let The quantity for type A coffee = a poundsAnd The quantity of type B coffee = b poundsNow, According to questiona + b = 167 pounds      And$ 5.70 × a + $ 4.30 × b = $ 820.30Now solving equations5.70 × ( a + b ) = 5.70 × 167 or, 5.70 a + 5.70 b = 951.9Now , ( 5.70 a + 5.70 b ) - (   5.70  a +  4.30  b ) = 951.9 - 820.30or, ( 5.70 a - 5.70 a ) + ( 5.70 b - 4.30 b ) = 131.6Or, 0 + 1.4 b = 131.6∴ b = [tex]\frac{131.6}{1.4}[/tex]I.e b = 94 poundsPut the value of b to get a valueSo, a = 167 pounds - bOr, a = 167 - 94 ∴   a = 73 poundsHence The quantity of type A coffee is 73 poundsAnd The quantity of type B coffee is 94 pounds   .  Answer