coffee shop plans to mix grage a cogge costing $9.50/lb and grade b coffee costing &7 /lb to yield a 20lb blen costing $8.50/lb. how many pounds of each to make the blend?
a=b=20
9.5a+7b=170
What is " grage a cogge "?
To solve this problem, you can use a system of equations. Let's assign the variables 'a' and 'b' to represent the number of pounds of grade A and grade B coffee used respectively.
Based on the given information, we have the following equations:
Equation 1: a + b = 20 (since the total weight of the blend is 20 lbs)
Equation 2: 9.5a + 7b = 170 (since the cost of the blend is $8.50 per pound and the total cost is $170)
We can solve this system of equations by substitution or elimination method.
Let's use the substitution method:
1. Solve Equation 1 for 'a':
a = 20 - b
2. Substitute the value of 'a' in Equation 2:
9.5(20 - b) + 7b = 170
Simplifying this equation:
190 - 9.5b + 7b = 170
-2.5b = -20
b = 8
Now that we have the value of 'b', we can substitute it back into Equation 1 to find 'a':
a + 8 = 20
a = 12
Therefore, to make the blend, the coffee shop needs 12 pounds of grade A coffee and 8 pounds of grade B coffee.