Question

Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost $7.70 per pound with French Roast Columbian coffee that cost $8.60 per pound to make a 30-pound blend. Their blend should cost them $8.00 per pound. How much of each type of coffee should they buy?

Answer 1

To determine how much of each type of coffee Julia and her husband should buy, we can set up a system of linear equations to represent the costs of the two types of coffee in their blend and the total cost of the blend. Let x represent the number of pounds of City Roast coffee and y represent the number of pounds of French Roast coffee. Then, we have:

7.70x + 8.60y = 8.00(x + y) (the total cost of the blend)
x + y = 30 (the total weight of the blend)

We can use substitution or elimination method to solve this system of equations. Using substitution, we can solve for one variable in terms of the other and then substitute into the second equation. For example, we can solve for y in terms of x:

y = 30 - x

And substitute into the first equation:

7.70x + 8.60(30 - x) = 8.00(30)
7.70x + 258.00 - 8.60x = 240.00
-1.90x = -18.00
x = 9.47 pounds

This means that Julia and her husband should buy 9.47 pounds of City Roast coffee and 20.53 pounds of French Roast coffee to make their 30-pound blend at a cost of $8.00 per pound.