Christine's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Christine $5.85 per pound, and type B coffee costs
$4.40 per pound. This month, Christine made
174 pounds of the blend, for a total cost of
$906.25. How many pounds of type A coffee did she use?
if there are a lbs of A, then the rest (174-a) is B. So,
5.85a + 4.40(174-a) = 906.25
the actual answer is 26.
36789
Well, I don't want to be a "groundskeeper" here, but let's brew up the solution!
Let's assume that Christine used "x" pounds of type A coffee and "174 - x" pounds of type B coffee in her blend.
The cost of type A coffee can be calculated as $5.85 * x, and the cost of type B coffee can be calculated as $4.40 * (174 - x).
So, we have the equation:
$5.85x + $4.40(174 - x) = $906.25
Now, let's grind through this equation together!
$5.85x + $765.60 - $4.40x = $906.25
Combining like terms, we get:
$1.45x + $765.60 = $906.25
Next, subtract $765.60 from both sides:
$1.45x = $906.25 - $765.60
Simplifying, we have:
$1.45x = $140.65
Dividing both sides by $1.45, we find:
x = 97 pounds
So, Christine used 97 pounds of type A coffee in her blend. Now she can enjoy a strong cup of success!
To solve this problem, we can set up a system of equations.
Let's represent the pounds of type A coffee used as 'x' and the pounds of type B coffee used as 'y'.
According to the information given, we know:
The cost of type A coffee per pound, which is $5.85
The cost of type B coffee per pound, which is $4.40
The total cost of the blend, which is $906.25
Using this information, we can set up the following equations:
Equation 1: x + y = 174 (since the total pounds of the blend is 174 pounds)
Equation 2: 5.85x + 4.40y = 906.25 (since the total cost of the blend is $906.25)
Now, we can solve these equations to find the value of x (pounds of type A coffee).
To solve the equations, we can use substitution or elimination method. Here, let's use the substitution method.
From Equation 1, we can write y = 174 - x.
Now substitute y in Equation 2:
5.85x + 4.40(174 - x) = 906.25
Simplify the equation:
5.85x + 765.6 - 4.40x = 906.25
Combine like terms:
1.45x + 765.6 = 906.25
Subtract 765.6 from both sides:
1.45x = 140.65
Divide both sides by 1.45:
x ≈ 97.068
So, Christine used approximately 97.068 pounds of type A coffee.