Question

Hong's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Hong $5.75 per pound, and type B coffee costs $4.10 per pound. This month, Hong made 170 pounds of the blend, for a total cost of $858.70. How many pounds of type A coffee did he use?

Answer 1

98 pounds

Explanation:

Let A be pounds of A-type coffee and B be pounds of B-type coffee.

We can set-up two equations and solve simultaneously.

"This month, Hong made 170 pounds of the blend":

`A+B=170`

"Type A coffee costs Hong $5.75 per pound, and type B coffee costs $4.10 per pound ... a total cost of $858.70":

`5.75A+4.10B=858.70`

Now we can multiply first equation by -5.75 and then ADD UP this new equation and equation 2 to get B. We have:

`(-5.75)*(A+B=170)\\-5.75A-5.75B=-977.5`

Now solving for B:

`-5.75A-5.75B=-977.5\\5.75A+4.10B=858.70\\-------------\\-1.65B=-118.8\\B=72`

B = 72

Now plugging in this value into B of original first equation and solving for A gives us:

`A+B=170\\A+72=170\\A=170-72\\A=98`

Thus, he used 98 pounds of Coffee A.