Laura's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Laura $5.90 per pound, and Type B coffee costs $4.60 per pound. This month, Laura made 157 pounds of the blend, for a total cost of $805.40. How many pounds of Type A coffee did she use?

A) 80 pounds
B) 90 pounds
C) 100 pounds
D) 110 pounds

To solve this problem, we can set up a system of equations. Let x represent the pounds of Type A coffee used and y represent the pounds of Type B coffee used. We know that the cost of Type A coffee is $5.90 per pound and the cost of Type B coffee is $4.60 per pound. The total cost of the blend is $805.40. Therefore, we can write the following equations:

x + y = 157 (equation 1)
5.90x + 4.60y = 805.40 (equation 2)

We can solve this system of equations using substitution or elimination. Let's use the elimination method. Multiply equation 1 by 4.60 and equation 2 by -1. This gives us:

4.60x + 4.60y = 725.20 (equation 3)
-5.90x - 4.60y = -805.40 (equation 4)

Add equations 3 and 4 together to eliminate y:

-1.30x = -80.20
x = 80

Therefore, Laura used 80 pounds of Type A coffee.

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