Milan's Coffee Shop makes a blend that is a mixture of coffee types A and B. In one bag of the blend, there are 4 kilograms of type A. Six bags of the blend are a total of 48 kilograms. How many kilograms of type B are there in one bag?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 4, 6, and 48. Let b represent the number of kilograms of type B in one bag.
(b) Solve the equation in part (a) to find the number of kilograms of type B in one bag.
Answers
Step-by-step explanation:
We need to set up two expressions with two variables to answer this question. First let's set up the relationship that accounts for the unit cost of the coffees and the total cost for the blend.
5.65*A + 4.25*B = 717.6Let x = type A coffee at $5.65/lb
Let y = type B coffee at $4.25/lb
3x = y
5.65x + 4.25y = 717.60 Multiply this equation by 100
565x + 425y = 71760 Replace y with 3x
565x + 425(3x) = 71760
565x + 1275x = 71760
1840x = 71760
x = 39 pound of Type A coffee
y = 3x
y = 3(39)
y = 117 pounds of Type B coffee
Then we need an expression that compares the amount of each coffee used for the blend. Since three times of B was used, we can write the expression
3A = B
Take this and plug in 3A for B in the first expression so you get
5.65*A + 4.25*3A = 717.6
Work it through and simplify. You get 18.4*A = 717.6. Divide 18.4 into 717.6 to get 39 lb of coffee A was used.