Answer :
Final answer:
Laura used 80 pounds of Type A coffee.
Explanation:
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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