We appreciate your visit to Latoya s Coffee Shop makes a blend that is a mixture of two types of coffee Type A coffee costs Latoya 4 35 per pound. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The quantity of type A coffee Latoya used is approximately 87.61 pounds.
How do we find the quantity of type A coffee Latoya used in the blend?
To find out the quantity of type A coffee Latoya used in the blend, we shall set up a system of equations based on the given information.
Let us take:
The number of pounds of type A coffee used =x
The number of pounds of type B coffee used = y.
We know that the total pounds of the blend is 139 pounds, so we have:
x + y = 139
Recall that:
The total cost of the blend = $666.75,
The cost of type A coffee = $4.35 per pound,
The cost of type B coffee is $5.50 per pound.
So, we shall write another equation for the total cost:
4.35x + 5.50y = 666.75
Let us solve this system of equations by solving for x in the first equation:
x = 139 - y
Next, we replace the expression for x into the second equation:
4.35(139 - y) + 5.50y = 666.75
Then, simplify and solve for y:
607.65 - 4.35y + 5.50y = 666.75
Combine like terms:
1.15y = 666.75 - 607.65
1.15y = 59.10
Divide by 1.15 to find the value of y:
y = 59.10 / 1.15
y ≈ 51.39
So, Latoya used approximately 51.39 pounds of type B coffee.
To find the amount of type A coffee, place this value back into the first equation:
x + 51.39 = 139
Solve for x:
x = 139 - 51.39
x ≈ 87.61
Thus, Latoya used approximately 87.61 pounds of type A coffee in the blend.
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