Word problems confuse me.
THe owner of a fancy food shoppe wants to mix cashews selling at $8/kg and pecans selling at $7/kg. How many kg of each kind of nuts should be mixted to get 8 kg worth $7.25/kg?
$8/kg*Xkg + $7kg*Ykg = 7.25/kg*8kg,
Eq1: 8X + 7Y = 58,
Eq2: X + Y = 8,
Multiply Eq2 by -8, add the 2 Eqs and get:
-Y = -6,
Y = 6kgs of pecans.
Substitute 6 for Y in Eq2 :
X + 6 = 8,
X = 2 kgs of cashews.
Ah, word problems! They can be as nutty as a mixed bag of cashews and pecans. Well, worry not, my friend, for Clown Bot is here to help crack this problem wide open!
Let's solve this together. We need to find the quantities of cashews and pecans to mix in order to obtain the desired value. Let's say we need 'x' kilograms of cashews and 'y' kilograms of pecans.
Now, the cost of cashews is $8 per kilogram, so the total cost of cashews will be 8x dollars. Similarly, the total cost of pecans will be 7y dollars.
Since we want a total of 8 kilograms worth $7.25/kg, the total cost will be 8 * $7.25 = $58.
So, we can set up two equations to represent the problem:
Equation 1: 8x dollars + 7y dollars = $58 (equation for the total cost)
Equation 2: x + y = 8 (equation for the total weight)
Now, let's solve these equations with the help of Clown Bot's magical math skills!
Equation 2 tells us that x + y = 8. Let's rearrange it to express x in terms of y: x = 8 - y.
Substitute this value of x into Equation 1:
8(8 - y) + 7y = 58
Expand and simplify:
64 - 8y + 7y = 58
-y = -6
y = 6
Now, substitute the value of y back into Equation 2 to find x:
x + 6 = 8
x = 2
Voila! We've found our solution. You should mix 2 kilograms of cashews with 6 kilograms of pecans to get the desired mix.
Remember, mathematics can be nutty sometimes, but with a little laughter and some logical thinking, we can tackle any problem!
To solve this problem, we can set up a system of equations. Let's assume that x represents the number of kilograms of cashews and y represents the number of kilograms of pecans.
From the problem, we can deduce the following information:
1. The total weight of the mixture is 8 kg.
x + y = 8
2. The average price of the mixture is $7.25/kg.
(8x + 7y) / 8 = 7.25
Let's solve the system of equations to find the values of x and y.
To solve this problem, we can use a system of equations. Let's assume x represents the number of kilograms of cashews to be mixed and y represents the number of kilograms of pecans to be mixed.
We are given three conditions:
1. The total weight of the mixture is 8 kg: x + y = 8
2. The cost per kg of the mixture is $7.25: ((8 * 7.25) = (8x + 8y))
3. Cashews cost $8/kg and pecans cost $7/kg: 8x + 7y = 8 * 7.25
We can use these equations to solve for the values of x and y.
First, let's solve equation 1 for x by subtracting y from both sides:
x = 8 - y
Substitute this value of x into equation 3:
8(8 - y) + 7y = 8 * 7.25
Now we can solve for y:
64 - 8y + 7y = 58
Combine like terms:
-y = -6
Multiply both sides by -1 to isolate y:
y = 6
Substitute this value of y into equation 1 to solve for x:
x + 6 = 8
x = 2
Therefore, you will need 2 kg of cashews and 6 kg of pecans to get an 8 kg mixture worth $7.25/kg.