SOLUTION: a grocer buys cashews for $9 per kg and peanuts for $4.50 per kg. She wants to sell nuts individually, and she also makes 12 kg of a peanut-cashew mix which costs him $6 per kg. Ho
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Question 1154855: a grocer buys cashews for $9 per kg and peanuts for $4.50 per kg. She wants to sell nuts individually, and she also makes 12 kg of a peanut-cashew mix which costs him $6 per kg. How many kg of nut does the grocer require to make the mix? Found 2 solutions by mananth, greenestamps:Answer by mananth(16946) (Show Source):
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a grocer buys cashews for $9 per kg and peanuts for $4.50 per kg. She wants to sell nuts individually, and she also makes 12 kg of a peanut-cashew mix which costs him $6 per kg. How many kg of nut does the grocer require to make the mix?
let cashews bought be x kg
and nuts bought be y kg
x+y=12...……………….1
9x+4.5y = 6(x+y)
9x +4.5y = 6x +6y
3x-1.5y =0
multiply (1) by 1.5
1.5x+1.5y=18..... (2)
Add (1) & (2)
4.5x =18
x=4 kg
y= 8 kg
If a formal algebraic solution is not required, here is a quick and easy way to the solution to this or any other mixture problem involving two ingredients.
The target price of $6 per kg is 1/3 of the way from the $4.50 per kg price of the peanuts to the $9 per kg price of the cashews. (Picture the three prices on a number line; 6.00 is 1/3 of the way from 4.50 to 9.00.)
That means 1/3 of the mixture must be the more expensive cashews.
ANSWER: 1/3 of the 12kg, or 4kg, of cashews; 8 kg of peanuts.
