Lucy’s Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lucy $5.95 per pound, and type b coffee costs $4.65 per pound. This month, Lucy made 147 pounds of the blend, for a total cost of $803.15. How many pounds of type A did she use?
Let's assume that Lucy used x pounds of type A coffee in the blend.
Then, the rest of the blend (147-x) pounds must be type B coffee.
The cost of the type A coffee used in the blend is 5.95x, and the cost of the type B coffee used in the blend is 4.65(147-x).
The total cost of the blend is given as $803.15, so we can write the equation:
5.95x + 4.65(147-x) = 803.15
Simplifying and solving for x:
5.95x + 682.55 - 4.65x = 803.15
1.3x = 120.6
x = 92
Therefore, Lucy used 92 pounds of type A coffee in the blend. The rest of the blend (147-92 = 55 pounds) must be type B coffee.
Let's assume that Lucy used x pounds of type A coffee.
Since the total blend is 147 pounds, the amount of type B coffee used would be (147 - x) pounds.
The cost of type A coffee is $5.95 per pound, so the cost of x pounds of type A coffee would be 5.95x dollars.
The cost of type B coffee is $4.65 per pound, so the cost of (147 - x) pounds of type B coffee would be 4.65(147 - x) dollars.
According to the problem, the total cost of the blend is $803.15, so we can set up the equation:
5.95x + 4.65(147 - x) = 803.15
Now let's solve this equation step-by-step:
5.95x + 4.65(147 - x) = 803.15
5.95x + 683.55 - 4.65x = 803.15 (distribute 4.65)
1.3x + 683.55 = 803.15 (combine like terms)
1.3x = 803.15 - 683.55 (subtract 683.55 from both sides)
1.3x = 119.6 (simplify)
x = 119.6 / 1.3 (divide both sides by 1.3)
x ≈ 92 (simplify)
Therefore, Lucy used approximately 92 pounds of type A coffee.