The vendor of a coffee cart mixes coffee beans that cost $7 per pound with coffee beans that cost $5 per pound. How many pounds of each should be used to make a 50-pound blend that sells for $5.79 per pound?
If x lbs at $7, then
7x + 5(50-x) = 5.79(50)
To solve this problem, we can set up a system of linear equations based on the information given:
Let's assume that the vendor needs x pounds of coffee beans that cost $7 per pound and y pounds of coffee beans that cost $5 per pound to make the 50-pound blend.
The cost of the coffee beans can be calculated by multiplying the pounds of each type of coffee beans by their respective costs per pound and then adding them together. So, we have:
7x + 5y = total cost
Given that the blend sells for $5.79 per pound, the total revenue earned from the 50-pound blend can be calculated by multiplying the cost per pound by the total weight. This can be expressed as:
5.79 * 50 = total cost
Now, we have a system of equations:
7x + 5y = 5.79 * 50 (equation 1)
x + y = 50 (equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution here:
From equation 2, we can express x in terms of y:
x = 50 - y
Now, substitute this value of x into equation 1:
7(50 - y) + 5y = 5.79 * 50
Simplifying and solving for y:
350 - 7y + 5y = 289.5
-2y = 289.5 - 350
-2y = -60.5
Dividing both sides by -2, we get:
y = -60.5 / -2
y = 30.25
So, the vendor should use 30.25 pounds of coffee beans that cost $5 per pound and the remaining weight of the blend (50 - 30.25 = 19.75 pounds) should be filled with coffee beans that cost $7 per pound to make a 50-pound blend that sells for $5.79 per pound.