Question

Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost $14.80 per pound with French Roast Columbian coffee that cost $4.80 per pound to make a 50-pound blend. Their blend should cost them $5.00 per pound. How much of each type of coffee should they buy?

Answer 1

Julia and her husband should buy 20 pounds of City Roast coffee and 30 pounds of French Roast coffee.

Explanation:

Let x be the amount of City Roast coffee and y be the amount of French Roast coffee. We know that:

x + y = 50 (total amount of coffee is 50 pounds)

14.80x + 4.80y = 250 (total cost of the blend is $250)

5.00(x + y) = 250 (the blend should cost $5.00 per pound)

From the last equation, we have 5.00x + 5.00y = 250, which can be rearranged as:

5.00x - 250 = -5.00y

Now we can substitute the second equation into the first equation to find the amount of City Roast coffee:

14.80x + 4.80y = 250

14.80x + 4.80y = 250

14.80x - 250 = 4.80y - 5.00y

14.80x - 250 = -0.20y

y = (14.80x - 250) / -0.20

Substituting this expression for y into the first equation, we get:

x + (14.80x - 250) / -0.20 = 50

Solving for x, we find that x = 20.

Therefore, Julia and her husband should buy 20 pounds of City Roast coffee and 30 pounds of French Roast coffee.