At The Old Home Filler Up and Keep on aTruckin Cafe Mavis mi

At The Old Home Fill\'er Up and Keep on a-Truckin\' Cafe, Mavis mixes two different types of coffee beans to produce a house blend. The first type costs $2 per pound and the second costs $7 per pound. How much of each type does Mavis use to make 75 pounds of a blend which costs $4 per pound? (If the system is dependent assign the free variable the parameter t.) $2 per lb coffee lb $7 per lb coffee lb

Solution

Let x = lbs of $2 per lb coffee

y = lbs of $7 per lb coffee

Then

x+ y = 75 ... (1)

2x + 7y = 4 (x+y)

2x+7y = 4(75) (Using (1))

2x+7y = 300

2x + 7 (75-x) = 300 (Using (1))

2x + 525 -7x = 300

-5x + 525 = 300

-5x = -225

x = -225/-5 = 45

From (1),

45+y = 75

y = 75 - 45 = 30

So x= 45 lb and y=30 lb