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

To find the pounds of each kind of coffee that went into the mixture, we can set up a system of equations based on the given information. By using the substitution method, we can determine that approximately 2.5 pounds of Kenyan coffee and 4.5 pounds of Sri Lankan coffee went into the mixture.

Step-by-step explanation:

Let's assume the customer purchased x pounds of Kenyan coffee and y pounds of Sri Lankan coffee.

According to the given information, the cost of 1 pound of Kenyan coffee is $3.50 and the cost of 1 pound of Sri Lankan coffee is $5.60.

The total cost of the blend is $33.95 and the total weight of the blend is 7 pounds. We can set up the following system of equations:

x + y = 7 (equation 1)

3.50x + 5.60y = 33.95 (equation 2)

To solve this system of equations, we can use the substitution method:

From equation 1, we can express x in terms of y: x = 7 - y

Substituting x in equation 2:

3.50(7 - y) + 5.60y = 33.95

24.50 - 3.50y + 5.60y = 33.95

24.50 + 2.10y = 33.95

2.10y = 9.45

y ≈ 4.5

Substituting y back into equation 1:

x + 4.5 = 7

x ≈ 2.5

Therefore, approximately 2.5 pounds of Kenyan coffee and 4.5 pounds of Sri Lankan coffee went into the mixture.

Answer 2

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.