Question

Sarah Meeham blends coffee for tasti delight she needs to prepare 110 pounds of blended coffee beans selling for 4.45 per pound she plans to do this by blending together a high quality been costing 5.00 per pound and cheaper bean at 3.00 per pound

Answer 1

To find the amount of high-quality coffee beans needed, set up the equation: x + y = 110, where x is the pounds of high-quality coffee beans and y is the pounds of cheaper coffee beans. Use the equation 5x + 3y = 4.45(110). Solve this system of equations to find that Sarah needs 77.75 pounds of high-quality coffee beans and 32.25 pounds of cheaper coffee beans.

Step-by-step explanation:

To find the amount of the high quality coffee beans needed, we can set up the equation: x + y = 110, where x is the pounds of high quality coffee beans and y is the pounds of cheaper coffee beans. We also know that the cost of the high quality coffee beans is $5 per pound and the cost of the cheaper coffee beans is $3 per pound. So, the total cost equation becomes: 5x + 3y = 4.45(110).

Simplifying the second equation, we get: 5x + 3y = 485.5. Now we can solve this system of equations using substitution or elimination method. Let's use the substitution method:

1. From the first equation, we can solve for x in terms of y: x = 110 - y.
2. Substitute this value of x in the second equation: 5(110 - y) + 3y = 485.5.
3. Simplify and solve for y: 550 - 5y + 3y = 485.5. Combine like terms: -2y = -64.5. Divide both sides by -2: y = 32.25.
4. Substitute this value of y back into the first equation to find x: x = 110 - 32.25 = 77.75.

Therefore, Sarah needs 77.75 pounds of high quality coffee beans and 32.25 pounds of cheaper coffee beans to make 110 pounds of blended coffee beans.

Answer 2

Sarah Meeham should use 162.78 pounds of high-quality beans and 272.78 pounds of cheaper beans to prepare 110 pounds of blended coffee beans.

How to find the combination of coffee for tasti delight she needs to prepare 110 pounds of blended coffee

Let:

x represent the number of pounds of high-quality beans and

y represent the number of pounds of cheaper beans.

x + y = 110 .....eqn(1)

We can set up the equation for the total cost of the blended coffee beans:

5x + 3y = 4.45......eqn(2)

We can solve for x and y using substitution method of equation

Using Substitution method of equation

Solve the first equation for x:

x = 110 - y

Substitute this expression for x in the second equation:

5(110 - y) + 3y = 4.45

Expand and simplify:

550 - 5y + 3y = 4.45

Combine like terms:

-2y = 545.55

Solve for y:

y = 272.78

Substitute this value back into the equation x + y = 110 to solve for x:

x + 272.78 = 110

x = - 162.78

Therefore, Sarah Meeham should use 162.78 pounds of high-quality beans and 272.78 pounds of cheaper beans to prepare 110 pounds of blended coffee beans.