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

$5.80

per pound, and type B coffee costs

$4.10

per pound. This month, Hans made

117

pounds of the blend, for a total cost of

$569.80

. How many pounds of type A coffee did he use?

He used 53 pounds. I got this by using two equations.

a+b=117

and

5.8a+4.1b = 569.8

I took the first equation and subtracted 'b' so the equation looked like a=117-b.

I then plugged in 117-b into the second equation, so it ended up looking like this:

5.8 (117-b) = 569.8

5.8 times 117 is 678.6. And 5.8 times negative b is negative 5.8b.

The equation now looks like this:

678.6-5.8b+4.1b=569.8

Add like terms

678.6-1.7b=569.8

Then subtract 678.6 from both sides

-1.7b = - 108.8

divide each side by - 1.7

you get b = 64.

But because you are looking for how many pounds for a, subtract 64 from 117. You get 53. 53 is the answer.