High School

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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?

Answer :

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.

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Rewritten by : Barada