kristin and rob are selling pies for a school fundraiser. customers can buy blueberry cookies and blackberry cookies in boxes of 12. they sold blueberry cookies $9 a box and blackberry cookies for $12 a box. they earned $385 for 36 boxes of cookies. what js the cost of one box of blueberry cookies and one box of blackberry cookies?
Let's assume the number of boxes of blueberry cookies sold is x and the number of boxes of blackberry cookies sold is y.
From the problem, we have two equations:
1. x + y = 36 (the total number of boxes sold is 36)
2. 9x + 12y = 385 (the total amount earned from selling the cookies is $385)
To solve these equations, we can use substitution or elimination method.
Let's use the substitution method:
From equation 1, we have x = 36 - y.
Substituting this value of x in equation 2, we get:
9(36 - y) + 12y = 385
324 - 9y + 12y = 385
-9y + 12y = 385 - 324
3y = 61
y = 61/3 = 20.33 (rounded to 2 decimal places)
Substituting the value of y in equation 1, we get:
x + 20.33 = 36
x = 36 - 20.33 = 15.67 (rounded to 2 decimal places)
So, they sold approximately 15 boxes of blueberry cookies and 20 boxes of blackberry cookies.
Now, let's find the cost of one box of each type of cookie:
The cost of one box of blueberry cookies is $9.
The cost of one box of blackberry cookies is $12.
Therefore, the cost of one box of blueberry cookies is $9 and the cost of one box of blackberry cookies is $12.
Let's assume x represents the number of blueberry cookie boxes sold by Kristin and Rob, and y represents the number of blackberry cookie boxes sold.
We are given the following information:
- The cost of one box of blueberry cookies is $9.
- The cost of one box of blackberry cookies is $12.
- They earned a total of $385 from selling 36 boxes in total.
From the given information, we can set up a system of equations to solve for x and y:
Equation 1: x + y = 36 (as they sold a total of 36 boxes)
Equation 2: 9x + 12y = 385 (the total earnings from selling the boxes)
To solve this system of equations, we can multiply Equation 1 by 9 to match the coefficients of x in both equations.
9(x + y) = 9(36)
9x + 9y = 324
Now we have two equations:
9x + 9y = 324
9x + 12y = 385
Subtracting the first equation from the second equation, we can eliminate x:
(9x + 12y) - (9x + 9y) = 385 - 324
3y = 61
y = 61/3
y = 20.33 (approximately)
Since we can only have whole numbers of boxes, it means that y must be 20 (to have a whole number).
Substituting the value of y back into Equation 1, we can find the value of x:
x + 20 = 36
x = 36 - 20
x = 16
Therefore, they sold 16 boxes of blueberry cookies and 20 boxes of blackberry cookies.
To find the cost of one box of each type of cookie:
Cost of one box of blueberry cookies = $9
Cost of one box of blackberry cookies = $12
So, the cost of one box of blueberry cookies is $9, and the cost of one box of blackberry cookies is $12.
To find the cost of one box of blueberry cookies and one box of blackberry cookies, we need to set up a system of equations based on the given information.
Let's assume the cost of one box of blueberry cookies is 'x', and the cost of one box of blackberry cookies is 'y'.
From the problem, we know that customers can buy blueberry cookies and blackberry cookies in boxes of 12, and they sold a total of 36 boxes of cookies. We can write this as:
Blueberry Cookies: (x/12) * Number of boxes = Total Cost of Blueberry Cookies
Blackberry Cookies: (y/12) * Number of boxes = Total Cost of Blackberry Cookies
Since they earned $385 for 36 boxes of cookies:
(x/12) * 36 + (y/12) * 36 = 385
To solve this system of equations, we can simplify it further:
3x + 3y = 385
Now, we can solve this equation to find the values of 'x' and 'y', which will give us the cost of one box of blueberry cookies and one box of blackberry cookies.