CASHEWS $8.00 PER KILOGRAM AND PECANS $9.00 PER KILOGRAM, HOW MANY KILOGRAMS OF EACH TO MAKE 10 KILOGRAMS THAT COST $8.40
x= # kg of cashews
10-x = # kg of pecans
($8)(x) + ($9)(10-x) = $8.40
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Let's assume x kilograms of cashews are bought, and y kilograms of pecans are bought.
According to the given information, cashews cost $8 per kilogram and pecans cost $9 per kilogram.
The total weight of the cashews and pecans is 10 kilograms. So,
x + y = 10 (Equation 1)
The total cost of the cashews and pecans is $8.40. So,
8x + 9y = 8.40 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution to solve the system of equations.
From Equation 1, we can express x as:
x = 10 - y
Substituting this value of x into Equation 2, we get:
8(10 - y) + 9y = 8.40
Expanding and simplifying the equation:
80 - 8y + 9y = 8.40
80 + y = 8.40
y = 8.40 - 80
y = -71.60
Since the weight cannot be negative, this solution is not valid.
Hence, there is no solution in this case to buy 10 kilograms of cashews and pecans that costs $8.40.
To solve this problem, we can set up a system of equations.
Let's assume x represents the number of kilograms of cashews.
Similarly, let's assume y represents the number of kilograms of pecans.
From the given information, we can write two equations:
Equation 1: x + y = 10 (The sum of cashews and pecans is 10 kilograms)
Equation 2: 8x + 9y = 8.40 (The cost of cashews and pecans is $8.40)
To solve the system of equations, we can use the method of substitution or elimination. However, in this case, let's use the method of substitution:
Step 1: Solve Equation 1 for x in terms of y:
x = 10 - y
Step 2: Substitute the value of x in Equation 2:
8(10 - y) + 9y = 8.40
Simplifying the equation:
80 - 8y + 9y = 8.40
Combining like terms:
y = 0.40
Step 3: Substitute the value of y back into Equation 1 to find x:
x + 0.40 = 10
x = 9.60
Therefore, to make 10 kilograms of nuts that cost $8.40, you would need 9.60 kilograms of cashews and 0.40 kilograms (or 400 grams) of pecans.