SOLUTION: A grocer mixed peanuts(whose price is 90 cents per kilogram)with almonds(whose price is $1.10 per kilogram)to make a 20-kilogram mixture of nuts for sale at 98 cents per kilogram.

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Question 147690: A grocer mixed peanuts(whose price is 90 cents per kilogram)with almonds(whose price is $1.10 per kilogram)to make a 20-kilogram mixture of nuts for sale at 98 cents per kilogram. How many kilograms of peanuts and how many kilograms of almonds are in the mixture?
Found 2 solutions by mangopeeler07, stanbon:
Answer by mangopeeler07(462) About Me  (Show Source):
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With two variables------x=number of kilograms of 90cent peanuts and y=number of kilograms of 110cent almonds.
Set up an equation using the word problem: 90x%2B110y=98%2820%29 because the coefficients are the prices of the almonds and peanuts and the variable and 20 are the number of them. Then set up another equation x%2By=20 because the sum of the kilograms is 20. Then solve for x and get x=20-y. Plug that in the first equation and get 90%2820-y%29%2B110y=98%2820%29. Then distribute and get 1800-90y%2B110y=1960. Combine like terms and get 1800%2B20y=1960. Subtract 1800 from both sides and get 20y=160. Divide both sides by 20 and get y=8. Then plug 8 in for y in the second equation and get x%2B8=20. So x=12. So 8 kilograms of 110cent almonds and 12 kilograms of 90 cent peanuts is your final answer.


With one variable------x=number of kilograms of 90cent peanuts and 20-x=number of kilograms of 110cent almonds.90x%2B110%2820-x%29=98%2820%29
Distribute and get 90x%2B2200-110x=1960. Then combine like terms and get 2200-20x=1960. Subtract 2200 from each side and get -20x=-240. Divide both sides by 20 and get x=12. This is the number of kilograms of 90 cents peanuts. Then do 20-x or 20-12 and get 8. This is the number of kilograms of 110cent almonds. So 8 kilograms of 110cent almonds and 12 kilograms of 90 cent peanuts is your final answer.

Answer by stanbon(75887) About Me  (Show Source):
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A grocer mixed peanuts(whose price is 90 cents per kilogram)with almonds(whose price is $1.10 per kilogram)to make a 20-kilogram mixture of nuts for sale at 98 cents per kilogram. How many kilograms of peanuts and how many kilograms of almonds are in the mixture?
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EQUATIONS:
Quantity: p + a = 20
Value: 90p + 110a = 98*20
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Rearrange:
9p + 11a = 196
9p + 9a = 180
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2a = 16
a = 8 (# of pounds of almonds in the mixture)
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p + 8 = 20
p = 12 (# of pounds of peanuts in the mixture)
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Cheers,
Stan H.