SOLUTION: If 15 pounds of tea and 10 pounds of coffee together cost $15.50, while 25 pounds of tea and 13 pounds of coffee at the same prices cost $24.55, find the price per pound of each.

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Question 882249: If 15 pounds of tea and 10 pounds of coffee together cost $15.50, while 25 pounds of tea and 13 pounds of coffee at the same prices cost $24.55, find the price per pound of each.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x, price of tea
y, price of coffee

15x+10y=15.50 and 25x+13y=24.55 account for the cost of each combination of the purchases. The 15.50 equation can be simplified by dividing left and right by 5:
3x+2y=3.1.

Substitution seems easiest method.
SYSTEM:
-
3x+2y=3.1
-
25x+13y=24.55

25x=24.55-13y
highlight_green%28x=%2824.55-13y%29%2F25%29
substitute:
3%2824.55-13y%29%2F25%2B2y=3.1
3%2824.55-13y%29%2B50y=25%2A3.1
3%2A24.55-39y%2B50y=25%2A3.1
11y%2B3%2A24.55=25%2A3.1
11y=25%2A3.1-3%2A24.55
11y=3.85
y=3.85%2F11
highlight%28y=0.35%29, dollars per pound, coffee. Use this to find the value for x.