a nut mixture is made from two types of nuts: one type selling for 7.50/kg the other selling for 9.50/kg what mass of each type of nut should ne included in a 3 kg mixture that sells for 25
If there are x kg of the 7.50 nuts, the rest (3-x) are 9.50
So, add up the cost of the amounts used. It must equal the final cost.
7.50x + 9.50(3-x) = 25.00
To solve this problem, we'll use a system of equations. Let's assume the mass of the first type of nuts (selling for 7.50/kg) in the mixture is x kg, and the mass of the second type of nuts (selling for 9.50/kg) is y kg.
1. We know that the total mass of the mixture is 3 kg:
x + y = 3
2. We also know that the cost of the mixture is $25/kg. The cost is calculated by multiplying the price per kilogram of each type of nut by its respective mass, and then summing those two amounts. So we can write:
(7.50*x) + (9.50*y) = 25
Now we have a system of equations:
x + y = 3
7.50*x + 9.50*y = 25
To solve this system, we can use either substitution or elimination method. Let's use the substitution method.
From the first equation, we can express x in terms of y:
x = 3 - y
Substitute this value of x into the second equation:
7.50*(3 - y) + 9.50*y = 25
22.50 - 7.50*y + 9.50*y = 25
2*y = 25 - 22.50
2*y = 2.50
y = 1.25
Now that we know y, we can substitute it back into the first equation to find x:
x + 1.25 = 3
x = 3 - 1.25
x = 1.75
Therefore, in a 3 kg mixture that sells for $25/kg, you should include 1.75 kg of type 1 nuts (selling for $7.50/kg) and 1.25 kg of type 2 nuts (selling for $9.50/kg).