A grocer mixes almonds which sell for 1.20/kg with 180kg of Brazil nuts which sell for 1.50/kg. How many kg of almonds must he use in order to sell the mixture for 1.28/kg?
If x kg of almonds, then we have
1.20*x + 1.50*180 = 1.28(x+180)
To find the number of kilograms of almonds needed, let's assume the grocer needs to use x kilograms of almonds.
The cost of almonds per kg is $1.20, and the cost of Brazil nuts per kg is $1.50. The grocer wants to sell the mixture for $1.28 per kg.
So, the cost of almonds used will be 1.20 x and the cost of Brazil nuts used will be 1.50 * 180 kg.
To maintain an average selling price of $1.28 per kg, the total cost of the mixture must equal the total weight of the mixture multiplied by $1.28.
The equation becomes:
(1.20x + 1.50 * 180) = (x + 180) * 1.28
Now, let's solve for x:
1.20x + 1.50 * 180 = 1.28(x + 180)
Expand the equation:
1.20x + 270 = 1.28x + 230.4
Rearrange the equation:
1.20x - 1.28x = 230.4 - 270
Combine like terms:
-0.08x = -39.6
Divide both sides by -0.08:
x = -39.6 / -0.08
x = 495
Therefore, the grocer needs to use 495 kilograms of almonds in order to sell the mixture for $1.28 per kg.