A customer in a coffee shop purchases a blend of two coffees: kenyan, costing $3.50 a pound, and sri lankan, costing $5.60 a pound. he buys 7 lb of the blend, which costs him $33.95. how many pounds of each kind went into the mixture?

We have to make a system of equations:

x + y = 7; where x stays for pounds of Kenyan coffee, and y stays for pounds of Sri Lankan coffee. And: 3.50 * x + 5.60 * y = 33.95 (total cost).

From the 1st equation: x = 7 - y. We have to substitute it into the 2nd equation:

3.50 * (7 - y) + 5.60 * y = 33.95

24.50 - 3.50 y + 5.60 y = 33.95

5.60 y - 3.50 y = 33.95 - 24.50

2.10 y = 9.45

y = 9.45 : 2.10

y = 4.5 lb; x = 7 - 4.5 = 2.5 lb.

Answer: 2.5 lb of Kenyan coffee and 4.5 lb of Sri Lankan.