We appreciate your visit to John s Coffee Shop makes a blend that is a mixture of two types of coffee Type A coffee costs John 4 70 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 :
By setting up a system of equations and using the elimination method, we can calculate that John used 85 pounds of type A coffee for his blend at the coffee shop.
To determine how many pounds of type A coffee John used for his blend, we need to set up a system of equations based on the given information.
Let x represent the number of pounds of type A coffee and y represent the number of pounds of type B coffee. The cost of type A coffee is $4.70 per pound, and the cost of type B coffee is $5.90 per pound.
We are given two pieces of information:
- The total weight of the blend is 181 pounds, so x + y = 181.
- The total cost of the blend is $967.10, so 4.70x + 5.90y = 967.10.
We can solve this system of equations using substitution or elimination. Let's opt for elimination this time. By multiplying the first equation by 4.70, we get 4.70x + 4.70y = 851.70. Now we subtract this equation from the second equation to eliminate x.
5.90y - 4.70y = 967.10 - 851.70
1.20y = 115.40
y = 96
Now we know there are 96 pounds of type B coffee. We can use this information to find the number of pounds of type A coffee:
x + 96 = 181
x = 181 - 96
x = 85
John used 85 pounds of type A coffee in his blend.
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Rewritten by : Barada
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
