SOLUTION: Nicole's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Nicole $5.75 per pound, and type B coffee costs $4.20 per pound. This month's blend

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Question 909681: Nicole's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Nicole $5.75 per pound, and type B coffee costs $4.20 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $367.90. 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 total cost for the two mixes is $367.9
4.2*x+5.75*y=367.9
We know that the mix at $4.2 has 2 times the amount at $5.75
We substitute for x
4.2*(2*y)+5.75*y=367.9
We multiply out
(8.4+5.75)*y=367.9
We combine like terms.
14.15*y=367.9
Isolate y
y= 26.00
y= 26.00 at $5.75
Calculate x
x=2*y
x= 52.00 at $4.2
Your total for x is 52.00
Your total for y is 26.00
Your total for x and y is 78.00
Total invested 52.00 + 26.00= 78.00
We check
4.2* 52.00+5.75* 26.00=367.9
218.40+ 149.50=367.9
367.9=367.9
Since this statement is TRUE and neither x nor y is negative then all is well.