Question

Lucien can buy 1 pound of Columbian coffee beans for $4.25. He can buy 1 pound of French Roast

coffee beans for $3.75. If he buys a 1 pound mixture of the two kinds of beans for $4.00, how much of
each kind of coffee bean does he buy?
.
Write a system of equations and then solve.
Make sure you show all your work. Guess and check solutions will not receive full credit

Answer 1

Lucien bought 0.5 pounds of Columbian coffee beans and 0.5 pounds of French Roast coffee beans to create a 1 pound mixture costing $4.00.

Step-by-step explanation:

To solve the problem about the mixture of Columbian and French Roast coffee beans that Lucien buys, we can set up two equations based on the given information. Let x represent the amount of Columbian coffee beans at $4.25 per pound, and y represent the amount of French Roast coffee beans at $3.75 per pound. Lucien buys a 1-pound mixture, so the total weight equation is x + y = 1.

The second equation is based on the total cost of the mixture, which is $4.00. The cost equation can be represented as 4.25x + 3.75y = 4.00.

Now we have a system of linear equations:

• x + y = 1 (total weight)
• 4.25x + 3.75y = 4.00 (total cost)

Subtract the first equation from the second equation after multiplying it by 3.75 to eliminate y:
4.25x + 3.75y = 4.00(-3.75)(x + y = 1)----------------------

0.5x = 0.25

Divide both sides by 0.5 to obtain x = 0.5, which means Lucien bought 0.5 pounds of Columbian beans. Substituting x into the first equation, we get 0.5 + y = 1, so y = 0.5, meaning Lucien also bought 0.5 pounds of French Roast beans.