Problem

Shen's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Shen \$4.40 per pound, and type B coffee costs $\$ 5.90$ per pound. This month, Shen made 152 pounds of the blend, for a total cost of $\$ 793.30$ How many pounds of type B coffee did he use?

Answer

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Answer

So, Shen used \(\boxed{83}\) pounds of type B coffee.

Steps

Step 1 :Let's denote the amount of type A coffee as 'a' and the amount of type B coffee as 'b'.

Step 2 :We know that the total amount of coffee is 152 pounds, so we can write this as an equation: \(a + b = 152\).

Step 3 :We also know that the total cost of the coffee is $793.30. Given that type A coffee costs $4.40 per pound and type B coffee costs $5.90 per pound, we can write this as another equation: \(4.4a + 5.9b = 793.30\).

Step 4 :We can solve this system of equations to find the values of 'a' and 'b'.

Step 5 :The solution to the system of equations is {a: 69.0000000000000, b: 83.0000000000000}.

Step 6 :So, Shen used \(\boxed{83}\) pounds of type B coffee.

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