Question

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?

Answer 1

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.