Teresa's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Ter

Celia Lucas

Celia Lucas

Answered question

2022-06-24

Teresa's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Teresa 5.65 dollars per pound, and type B coffee costs 4.35 dollars per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of 673.20 dollars.
Find how many pounds of type A coffee were used.

Answer & Explanation

Josie Stephenson

Josie Stephenson

Beginner2022-06-25Added 20 answers

Let x be the number of type A coffee and y be the number of type B coffee
So the cost of the two types of coffee is x = 5.65 dollars per pound, y = 4.35 dollars per pound
We know that this month's blend used three times as many pounds of type B coffee as type A,
Thus, 3 x = y (1)

Now, the total cost of the coffee is:
5.65 x + 4.35 y = 678.20 (2)

Put the value of y = 3 x in equation (2),
5.65 x + 4.35 ( 3 x ) = 673.20
5.65 x + 13.05 x = 673.20
18.7 x = 673.20
x = 673.20 18.7
x = 36   p o u n d s

Now, substitute the value of x = 36 in equation (1)
3 ( 36 ) = y
y = 108   p o u n d s
Therefore, the number of pounds of type A coffee is 36   p o u n d s.
Roland Waters

Roland Waters

Beginner2022-06-26Added 6 answers

Good job, thank you. I really like the detailed explanation

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