Austin's Coffee Shop makes a blendd that is a mixture of two types of coffee. Type a coffee costs bill $5.70 per pound and type b coffee costs $4.65 per pound. This month bill made 181 pounds of the blend, for a total cost of $943.50. How many pounds of type A coffee did he use?

He use 97 pound of type A coffee

Step-by-step explanation:

Let's call A the pounds of type A coffee that Austin used this month and B the pounds of type B coffee that Austin used this month.

From the sentence: Type A coffee costs bill $5.70 per pound and type B coffee costs $4.65 per pound and the total cost is $943.50, we can formulated the equation 1 as:

5.70*A + 4.65*B=943.50

Because the total cost is the sum of the cost of every type of coffee.

Additionally, from the sentence: This month bill made 181 pounds of the blend, we can formulate the equation 2 as:

A + B = 181

Solving for B, we get:

B = 181 - A

Now, for find the value of A we need to replacing this last equation on equation 1, and solving for A as:

5.70*A + 4.65*B=943.50

5.70*A + 4.65 * (181-A) = 943.50

5.70*A + 841.65 - 4.65*A = 943.50

5.70*A - 4.65*A = 943.50 - 841.65

1.05*A = 101.85

A = 101.85/1.05

A = 97

So, this month, he use 97 pound of type A coffee.