Steve is making bags of mixed nuts. Almonds are $5 per pound & Cashews are $12 per pound. Steve charges $56 per 7 pound bag.
1. Write a system of equations that can be used to determine how many pounds of almonds & how many pounds of cashews Steve uses.
2. Solve the system of equations to determine how many pounds of almonds & cashews Steve uses.
So for #1 I've got it started like this:
A+C = 7
5A + 12C = 56
5(7-C)+12C = 56
35-5C+12C=56
Am I on the right path? Kinda stuck now?
Thanks!
1.X Lbs. of almonds.
Y Lbs. of cashews.
Eq1: x + y = 7
Eq2: 5x + 12y = 56.
2. Multiply Eq1 by -5 and add the Eqs.:
-5x - 5y = -35
+5x + 12y = 56
Sum: 7y = 21
Y = 3 Lbs.
In Eq1, replace Y with 3:
x + 3 = 7
X = 4 Lbs.
A+C = 7
5A + 12C = 56
5(7-C)+12C = 56
35-5C+12C=56
7C=21
C=3 lbs, A=2lbs
Steve is making bags of mixed nuts. Almonds are $5 per pound and cashews are $12 per pound. Steve charges $56 per 7 pound bag.
Yes, you are on the right path! You have correctly written the first equation:
A + C = 7
This equation represents the fact that the total weight of almonds (A) and cashews (C) used in a bag together is equal to 7 pounds.
Now let's move on to the second equation. You correctly set up the equation:
5A + 12C = 56
This equation represents the cost of the mixed nuts in a bag. The cost of almonds per pound is $5 (represented by 5A), and the cost of cashews per pound is $12 (represented by 12C). The total cost of the mixed nuts in a bag is $56.
Now, to solve the system of equations, you can use the method of substitution or elimination. I'll guide you through the elimination method.
To eliminate one of the variables, we need to manipulate the equations to have the same coefficient for either A or C. In this case, let's eliminate the variable A.
Multiply the first equation by 5 to match the coefficient of A in the second equation:
5(A + C) = 5(7)
5A + 5C = 35
Now, let's subtract the second equation from the first equation to eliminate A:
(5A + 5C) - (5A + 12C) = 35 - 56
5A - 5A + 5C - 12C = 35 - 56
-7C = -21
Now, divide both sides of the equation by -7 to solve for C:
C = (-21) / (-7)
C = 3
Now that we have the value of C, we can substitute it back into one of the original equations to find A. Let's use the first equation:
A + C = 7
A + 3 = 7
A = 7 - 3
A = 4
So, the solution to the system of equations is A = 4 and C = 3. This means Steve uses 4 pounds of almonds and 3 pounds of cashews in each 7-pound bag of mixed nuts.