Michael and Stephanie are selling cookies for a school fundraiser. Customers can by boxes of either chocolate chip or oatmeal cookies. Michael and 14 boxes of chocolate chip cookies and 6 boxes of oatmeal cookies for a total of $160. Stephanie sold 12 boxes of chocolate chip cookies and 12 boxes of oatmeal cookies for a total of $192. How much was each box of chocolate chip cookies and how much was each box of oatmeal cookies?
Overlooking your typos ....
14 c + 6 o = 160
12 c + 12 o = 192 ----> c + o = 16 or o = 16-c
plug into the first
14c + 6(16-c) = 160
solve for c, the sub into o = 16-c
Let's assume the cost of each box of chocolate chip cookies as "C" and each box of oatmeal cookies as "O".
From the information given:
Michael sold 14 boxes of chocolate chip cookies for a total of $160.
So, 14C = 160.
Similarly,
Michael sold 6 boxes of oatmeal cookies for a total of $160.
So, 6O = 160.
Stephanie sold 12 boxes of chocolate chip cookies for a total of $192.
So, 12C = 192.
Similarly,
Stephanie sold 12 boxes of oatmeal cookies for a total of $192.
So, 12O = 192.
Now we can solve these equations to find the cost of each box of chocolate chip cookies (C) and the cost of each box of oatmeal cookies (O).
From the first equation,
14C = 160
Dividing both sides by 14,
C = 160/14
C = 11.43 (approx)
From the second equation,
6O = 160
Dividing both sides by 6,
O = 160/6
O = 26.67 (approx)
From the third equation,
12C = 192
Dividing both sides by 12,
C = 192/12
C = 16
From the fourth equation,
12O = 192
Dividing both sides by 12,
O = 192/12
O = 16
So, the cost of each box of chocolate chip cookies is $16, and the cost of each box of oatmeal cookies is $26.67 (approx).
To solve this problem, we can consider using a system of equations. Let's denote the price of a box of chocolate chip cookies as "x" dollars and the price of a box of oatmeal cookies as "y" dollars.
From the information given, we can form two equations:
Equation 1: 14x + 6y = 160
Equation 2: 12x + 12y = 192
To solve this system of equations, we can use the method of substitution or elimination. In this case, let's use the method of elimination to solve for x and y.
Step 1: Multiply Equation 1 by 2 and Equation 2 by 3 to eliminate the x-terms.
Equation 1: 28x + 12y = 320
Equation 2: 36x + 36y = 576
Step 2: Subtract Equation 1 from Equation 2 to eliminate the x-terms.
(36x + 36y) - (28x + 12y) = 576 - 320
8x + 24y = 256
Step 3: Divide Equation 3 by 8 to solve for y.
(8x + 24y)/8 = 256/8
x + 3y = 32
Step 4: Multiply Equation 4 by 3 and subtract it from Equation 3 to eliminate the y-terms.
(3)(x + 3y) = (3)(32)
3x + 9y = 96
- (x + 3y) = -32
----------------
2x = 64
Step 5: Solve for x by dividing both sides of Equation 5 by 2.
2x/2 = 64/2
x = 32
Step 6: Substitute the value of x into Equation 4 to solve for y.
32 + 3y = 32
3y = 0
y = 0
Therefore, a box of chocolate chip cookies costs $32, and a box of oatmeal cookies costs $0.
However, note that the answer seems unusual since the price of a box of oatmeal cookies is $0. It's possible that there is an error in the given information, so it's worth double-checking the problem or seeking further clarification.