Miguel's coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $5.95

Question

per pound, and Type B coffee costs $4.65
per pound. This month's blend used three times as many pounds of Type B coffee as Type A, for a total cost of $796.00
. How many pounds of Type A coffee were used?
40
30
70
50

Answer 1

Let \( x \) be the number of pounds of Type A coffee. Since Miguel used three times as many pounds of Type B coffee as Type A, the amount of Type B coffee used would be \( 3x \) pounds.

Now we can set up an equation for the total cost of the coffee blend based on the given costs:

• The cost of Type A coffee is \( 5.95x \).
• The cost of Type B coffee is \( 4.65(3x) = 13.95x \).

The total cost of the blend is the sum of the costs of Type A and Type B:

\[ 5.95x + 13.95x = 796 \]

Combining the terms on the left:

\[ 19.90x = 796 \]

Now, we solve for \( x \):

\[ x = \frac{796}{19.90} \approx 40 \]

Therefore, the number of pounds of Type A coffee used is \( 40 \).

So, the answer is:

\[ \boxed{40} \]