Question

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 1

The quantity of type A coffee is 73 pounds

The quantity of type B coffee is 94 pounds .

Explanation:

Given as :

The price of Type A coffee costs = $ 5.70 per pound

The price of Type B coffee costs = $ 4.30 per pound

The total quantity of coffee does Reuben purchases = 167 pounds

The total cost of the coffee for 167 pounds = $ 820.30

Let The quantity for type A coffee = a pounds

And The quantity of type B coffee = b pounds

Now, According to question

a + b = 167 pounds And

$ 5.70 × a + $ 4.30 × b = $ 820.30

Now solving equations

5.70 × ( a + b ) = 5.70 × 167

or, 5.70 a + 5.70 b = 951.9

Now ,

( 5.70 a + 5.70 b ) - ( 5.70 a + 4.30 b ) = 951.9 - 820.30

or, ( 5.70 a - 5.70 a ) + ( 5.70 b - 4.30 b ) = 131.6

Or, 0 + 1.4 b = 131.6

∴ b =
`(131.6)/(1.4)`

I.e b = 94 pounds

Put the value of b to get a value

So, a = 167 pounds - b

Or, a = 167 - 94

∴ a = 73 pounds

Hence The quantity of type A coffee is 73 pounds

And The quantity of type B coffee is 94 pounds . Answer