SOLUTION: Bernice mixes peanuts worth 105.00 per kilo with 100 kilograms of cashew nuts worth 50.00 per kilo. How many kilograms of peanuts should be added so that the final mix is worth 75

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Question 950287: Bernice mixes peanuts worth 105.00 per kilo with 100 kilograms of cashew nuts worth 50.00 per kilo. How many kilograms of peanuts should be added so that the final mix is worth 75.00 per kilogram?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
peanuts = 105 per kilo
cashews = 50 per kilo
x = number of kilos of peanuts
100 = number of kilos of cashews.

total kilos = x + 100

105 * x + 100 * 50 = 75 * (x + 100)

simplify to get:

105x + 5000 = 75x + 7500

subtract 75x from both sides of the equation and subtract 5000 from both sides of the equation to get:

105x - 75x = 7500 - 5000

simplify to get:

30x = 2500

divide both sides of the equation by 30 to get:

x = 250/3

that's equivalent to 83 and 1/3 kilos of peanuts.

replace x in the original equation with 250/3 to confirm the solution is good.

105 * x + 100 * 50 = 75 * (x + 100) becomes:

105 * 250/3 + 100 * 50 = 75 * (250/3 + 100)

simplify to get:

8750 + 5000 = 6250 + 7500 which becomes:

13750 = 13750

this confirms the solution is good.