Question

Tammy's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tammy $9.95 per pound, and type B coffee costs $4.40 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $560.50. How many pounds of type A coffee were used?

Answer 1

Step 1 : we will name the number of pounds of type A coffee were used is letter x then

We also do the same name the number of pounds of type B coffee were used in letter y.

Step 2: we will find the hints to find x and y

Hint 1 : We have total cost of two type A and type B is $560.5.

Price per pound of Type A : $9.95

Price per pound of Type B : $4.40

Cost = price per pound * (multipe) number per pound .So we have an expression 1:

9.95 * x + 4.4*y = 560.5

Hint 2: This month's blend used twice as many pounds of type B coffee as type A . That means the number of pounds of type B is double than the the number of pounds of type A so we have a another expression 2:

y = 2*x (2)

Step 3: we have enough hints so we could find x (number of pounds of type A coffee)

We will pass the value of y = 2*x into the expression 1 so we get:

9.95 *x + 2*x*4.4 = 560.5

9.95x + 8.8x = 560.5

18.75x =560.5

x = 560.5 / 18.75

x = 29.89

The anwser is number of pounds of type A coffee is 29.89