A grocer mixes together some cashews costing 8$ per kilogram with some nuts costing 10$ per kilogram. The grocer sold 12 kg of the mixture for 8.50$ per kilogram. How many kilograms of cashews were in the mixture?
I have to find 2 equations then find the answer most likely using substitution.
thanks:)
In case anyone's wondering:
c= kg of cashews
n= kg of nuts
12 kg of $8.5 is $102
We can say that:
8c + 10n = 102
(first equation)
And also:
c + n = 12
(second equation)
We isolate a variable in the second equation:
n = 12 - c
Plug that into the first equation:
8c + 10(12 - c) = 102
Simplify:
8c + 120 - 10c = 102
Simplify:
-2c = -18
2c = 18
c = 9
Now that we know the value of c, we can plug that into the second equation to find the value of n.
9 + n = 12
n = 12 - 9
n = 3
FINAL ANSWER:
3 kg of nuts, 9 kg of cashews
Well, that's quite a nutty situation! Let's break it down, shall we?
Let's say the grocer mixed x kilograms of cashews with y kilograms of nuts. Since we're dealing with kilograms, we can set up the following equations:
1. Total Weight: x + y = 12 (equation for the total weight of the mixture)
2. Total Cost: (8x + 10y) / 12 = 8.50 (equation for the average cost per kilogram)
Now, let's solve this mystery by using substitution!
From equation 1, we find that x = 12 - y.
Plugging this into equation 2, we get:
(8(12 - y) + 10y) / 12 = 8.50
Let's simplify:
(96 - 8y + 10y) / 12 = 8.50
(96 + 2y) / 12 = 8.50
Multiply both sides by 12 to get rid of the pesky denominator:
96 + 2y = 8.50 * 12
96 + 2y = 102
Now, let's subtract 96 from both sides:
2y = 102 - 96
2y = 6
Finally, divide by 2:
y = 6 / 2
y = 3
So, the grocer mixed 3 kilograms of nuts. Since the total weight of the mixture is 12 kilograms, the amount of cashews must be x = 12 - y = 12 - 3 = 9 kilograms!
Voilà! The grocer mixed 9 kilograms of cashews in the mixture. Have a nut-tastic day!
Let's represent the number of kilograms of cashews in the mixture as x and the number of kilograms of nuts as y.
The cost of cashews per kilogram is $8, so the cost of x kilograms of cashews would be 8x dollars.
Similarly, the cost of nuts per kilogram is $10, so the cost of y kilograms of nuts would be 10y dollars.
The grocer sold a total of 12 kg of the mixture at $8.50 per kilogram, so the total cost of the mixture would be 12 * $8.50 = $102.
Therefore, we can set up the following two equations:
1. The cost equation: 8x + 10y = 102
2. The quantity equation: x + y = 12
To solve this system of equations, we can use the substitution method.
From equation 2, we can rewrite y = 12 - x.
Substituting y in equation 1 with the value from equation 2, we get:
8x + 10(12 - x) = 102
8x + 120 - 10x = 102
-2x + 120 = 102
-2x = 102 - 120
-2x = -18
Dividing both sides of the equation by -2, we have:
x = -18 / -2
x = 9
So, there were 9 kilograms of cashews in the mixture.
To solve this problem, let's assign variables to the unknown quantities:
Let's say the amount of cashews in the mixture is represented by "x" kilograms.
Now let's set up the first equation based on the cost of the cashews and the nuts in the mixture:
The cost of x kilograms of cashews at $8 per kilogram is 8x dollars.
The cost of (12 - x) kilograms of nuts (since the total mixture is 12 kg) at $10 per kilogram is 10(12 - x) dollars.
Therefore, the total cost of the mixture is 8x + 10(12 - x) dollars.
The second equation is based on the selling price of the mixture:
The grocer sold 12 kg of the mixture for $8.50 per kilogram, so the total revenue from the sale is 12 * 8.50 dollars.
Now to solve the problem, we can set up the equation:
Total cost of the mixture = Total revenue from the sale
8x + 10(12 - x) = 12 * 8.50
Now you can use substitution to solve this equation.
8x + 120 - 10x = 102
-2x + 120 = 102
-2x = 102 - 120
-2x = -18
x = (-18) / (-2)
x = 9
Therefore, there were 9 kilograms of cashews in the mixture.