Sarah blends coffee for Tasti-Delight. She needs to prepare 170 lbs of blended coffee beans selling for $3.59 per pound. She plans to do this by blending together a high-quality bean costing $5.00 per pound and a cheaper bean at $2.00 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee bean she should blend.

Question

Sarah blends coffee for Tasti-Delight. She needs to prepare 170 lbs of blended coffee beans selling for $3.59 per pound. She plans to do this by blending together a high-quality bean costing $5.00 per pound and a cheaper bean at $2.00 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee bean she should blend.

Answer 1

amount of expensive coffee --- x

amount of cheaper coffee --- 170-x

5x + 2(170-x) = 3.59(170)

should be easy to solve for x, then sub back in my definitions.

Answer 2

To find out how much high-quality coffee bean and how much cheaper coffee bean Sarah should blend, let's set up some equations.

Let's say Sarah needs to blend x pounds of high-quality coffee bean and y pounds of cheaper coffee bean.

The total weight of blended coffee beans is 170 lbs, so we have the equation:
x + y = 170 -- Equation 1

The cost per pound of the high-quality coffee bean is $5.00, and Sarah needs to blend x pounds of it. So, the cost of high-quality coffee bean is 5x dollars.

The cost per pound of the cheaper coffee bean is $2.00, and Sarah needs to blend y pounds of it. So, the cost of cheaper coffee bean is 2y dollars.

The total cost of blended coffee beans is the sum of the costs of each type of coffee bean, which is $3.59 per pound times 170 pounds:
3.59 * 170 = 611.30 dollars

So, we have the equation:
5x + 2y = 611.30 -- Equation 2

Now, we can solve the system of equations formed by Equation 1 and Equation 2 to find the values of x and y.

One way to solve this system of equations is by substitution:

Rearrange Equation 1 to solve for x:
x = 170 - y

Substitute this value of x into Equation 2:
5(170 - y) + 2y = 611.30

Simplify and solve for y:
850 - 5y + 2y = 611.30
-3y = -238.70
y = (-238.70)/(-3)
y ≈ 79.57

Since we want to find the nearest pound, let's round y to the nearest whole number:
y ≈ 80 lbs

Now, substitute this value of y back into Equation 1 to find x:
x + 80 = 170
x ≈ 90 lbs

So, Sarah should blend approximately 90 pounds of high-quality coffee bean and 80 pounds of cheaper coffee bean.