SOLUTION: well i have to change this problem to systems of linear equations lou wants to make a coffee mixture to sell. He is going to sumatra coffee which costs $2.50 per pound with colu

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Question 854899: well i have to change this problem to systems of linear equations
lou wants to make a coffee mixture to sell. He is going to sumatra coffee which costs $2.50 per pound with columbian coffee which costs $3.75 per pound. he wants to make 50 pounds of mix and he wants to cost of mix to be $3.35 per pound. of each will he need
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of pounds of sumatra at 2.50 per pound.
y = number of pounds of columbian at 3.75 per pound.
want a mix of both at 3.35 per pound.
total of both will be 50 pounds.

x + y = 50
2.50 * x + 3.75 * y = 3.35 * 50

simplify the second equation to get:

x + y = 50
2.5x + 3.75y = 167.5

multiply the first equation by -2.5 to get:

-2.5x - 2.5y = -2.5 * 50
2.5x + 3.75y = 167.5

simplify the first equation to get:

-2.5x -2.5y = -125
2.5x + 3.75y = 167.5

add the 2 equations together to get:

1.25y = 42.5

divide both sides of this equation to get:

y = 42.5 / 1.25 = 34

since x + y = 50, then x must be equal to 16.

you have:

x = 16
y = 34
x + y = 50

2.5x + 3.75y = 167.5
substitute 16 for x and 34 for y to get:
2.5 * 16 + 3.75 * 34 = 167.5
simplify to get:
167.5 = 167.5
this confirms the solution of x = 16 and y = 34 is good.