Cashew nuts are sold at $15.00/kg. Walnuts are sold at $12.00/kg. What quantities of each nut would a store owner put into a 100-kg barrel so that it could be sold for $13.20/kg?
----------------
15.00c+12.00w= 31.20
C+w= 100
Are these equations right?
15c + 12w = 13.20*100 = 1320.
Eq1: 15c + 12w = 1320.
Eq2: C + W = 100.
Multiply both sides of Eq2 by (-15) and add the Eqs.
Remember that C and W are in KGs.
The equations you have written are not correct.
Let's correct the equations:
Let's assume the store owner puts x kg of cashew nuts (C) and y kg of walnuts (W) into the 100-kg barrel.
Based on the price per kilogram, we can set up the equation:
15x + 12y = 13.20 * 100
Next, we need to include the constraint that the total quantity of nuts in the barrel is 100 kg:
x + y = 100
Now we have a system of equations:
15x + 12y = 13.20 * 100
x + y = 100
We can solve this system of equations to find the quantities of each nut that the store owner would put into the barrel.
Yes, the equations are correct.
Let's define the variables:
c = quantity of cashew nuts (in kg)
w = quantity of walnuts (in kg)
The first equation represents the total cost of the nuts, given their individual prices and quantities:
15.00c + 12.00w = 31.20
The second equation represents the total weight of the nuts in the barrel, which should be equal to 100 kg:
c + w = 100
Now, we have a system of two equations with two variables. To solve it, we can use the method of substitution or elimination. Let's use the method of substitution:
From the second equation, we can rewrite it as c = 100 - w.
Now, we substitute this expression for c in the first equation:
15.00(100 - w) + 12.00w = 31.20
Expanding and simplifying the equation:
1500 - 15w + 12w = 31.20
1500 - 3w = 31.20
Next, we solve for w:
-3w = 31.20 - 1500
-3w = -1468.80
w = (-1468.80) / (-3)
w ≈ 489.60
Now, substitute this value back into the second equation to solve for c:
c + 489.60 = 100
c = 100 - 489.60
c ≈ 10.40
Therefore, the store owner would put approximately 10.40 kg of cashew nuts and 489.60 kg of walnuts into the 100-kg barrel in order to sell it for $13.20/kg.