SOLUTION: Hans's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Hans $4.10 per pound, and type B coffee costs $5.35 per pound. This month's blend us

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Question 907145: Hans's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Hans $4.10 per pound, and type B coffee costs $5.35 per pound. This month's blend used three+times as many pounds of type B coffee as type A, for a total cost of $785.85 . How many pounds of type A coffee were used?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
We know that the cost for the two blends is $785.85
5.35*x+4.10*y=785.85
We know that the blend at $5.35 has 3 times the amount at $4.10
We substitute for x
5.35*(3*y)+4.10*y=785.85
We multiply out
(16.05+4.10)*y=785.85
We combine like terms.
20.15*y=785.85
Isolate y
y= 39
y= 39 lbs at $4.10
Calculate x
x=3*y
x=117 lbs at $5.35
Your total for x is 117 lbs
Your total for y is 39 lbs
Your total for x and y is 156 lbs
Total mixed 117 + 39=156 lbs
We check
5.35*117+4.10*39=785.85
625.95+159.90=785.85
785.85=785.85
Since this statement is TRUE and neither is negative then all is well.