John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?

By setting up a system of equations and using the elimination method, we can calculate that John used 85 pounds of type A coffee for his blend at the coffee shop.

To determine how many pounds of type A coffee John used for his blend, we need to set up a system of equations based on the given information.

Let x represent the number of pounds of type A coffee and y represent the number of pounds of type B coffee. The cost of type A coffee is $4.70 per pound, and the cost of type B coffee is $5.90 per pound.

We are given two pieces of information:

The total weight of the blend is 181 pounds, so x + y = 181.
The total cost of the blend is $967.10, so 4.70x + 5.90y = 967.10.

We can solve this system of equations using substitution or elimination. Let's opt for elimination this time. By multiplying the first equation by 4.70, we get 4.70x + 4.70y = 851.70. Now we subtract this equation from the second equation to eliminate x.

5.90y - 4.70y = 967.10 - 851.70
1.20y = 115.40
y = 96

Now we know there are 96 pounds of type B coffee. We can use this information to find the number of pounds of type A coffee:

x + 96 = 181
x = 181 - 96
x = 85

John used 85 pounds of type A coffee in his blend.