Daniel, Susan and Rick bought some cookies to sell. The cookies were sold at 6 for $2. Daniel sold 1/4 of the cookies. Susan sold 2/7 as many cookies as Rick. Daniel and Susan sold a total of 120 cookies.
a)How many cookies did they sell altogether?
b)How much did they collect from the cookies sold?
c)If the cookies costs $0.20 each, how much profit did they make from the sale?
X = total # of cookies bought.
X/4 = The # of cookies sold by Daniel.
Y = The # of cookies sold by Rick.
2Y/7 = The # of cookies sold by Susan.
X/4 + 2Y/7 = 120 = The # of cookies sold by Daniel and Susan.
Multiply both sides by 28:
Eq1: 7x + 8y = 3360.
y = x - 120,
Eq2: x - y = 120.
Multiply Eq2 by 8 and add to Eq1:
7x + 8y = 3360
8x - 8y = 960
Sum: 15x = 4320,
X = 288 = The # of cookies sold.
b. Amt = $2/6 * 288 = $96.
c. Cost = $.20 * 288 = $57.60.
Profit = $96 - $57.60 = $38.40.
To solve this problem, we need to break it down into steps. Let's start by finding the amount of cookies each person sold.
a) Let's denote the total number of cookies as C. Since Daniel sold 1/4 of the cookies and Susan sold 2/7 as many cookies as Rick, we can write the following equations:
Daniel's cookies: D = (1/4)C
Susan's cookies: S = (2/7)R
Rick's cookies: R = C - D - S
We also know that Daniel and Susan sold a total of 120 cookies, so we can write the equation:
D + S = 120
b) To find the total number of cookies sold (C), we can substitute the values of D and S from the previous equations into the equation D + S = 120:
(1/4)C + (2/7)R = 120
c) To find the total amount collected from the cookies sold, we need to multiply the number of cookies sold by the price per cookie. Since the cookies were sold at 6 for $2, the price per cookie is $2/6 = $1/3. So, the equation becomes:
Amount collected = (1/3) x C
d) To find the profit made from the sale, we need to subtract the cost of the cookies from the amount collected. Since each cookie costs $0.20, the cost of C cookies is 0.20 x C. So, the equation becomes:
Profit = Amount collected - Cost of cookies
Let's solve this problem step by step.
1. We have the equation D + S = 120. To find the values of D and S, we can use the equation D = (1/4)C and S = (2/7)R. Let's substitute these values into the equation D + S = 120:
(1/4)C + (2/7)R = 120
2. We know that R = C - D - S. Substitute this value into the previous equation:
(1/4)C + (2/7)(C - D - S) = 120
3. Simplify the equation:
(1/4)C + (2/7)(C - (1/4)C - (2/7)R) = 120
(1/4)C + (2/7)(3/4)C = 120
(1/4)C + (6/28)C = 120
(7/28)C + (6/28)C = 120
(13/28)C = 120
4. Solve for C:
C = (120 * 28) / 13
C ≈ 256
So, they sold a total of approximately 256 cookies.
To find the amount collected:
Amount collected = (1/3) x C
Amount collected = (1/3) x 256
Amount collected ≈ $85.33
Therefore, they collected approximately $85.33 from the cookies sold.
To find the profit, we need to subtract the cost of the cookies. The cost of C cookies is 0.20 x C, so:
Profit = Amount collected - Cost of cookies
Profit = $85.33 - (0.20 x 256)
Profit ≈ $85.33 - $51.20
Profit ≈ $34.13
Therefore, they made a profit of approximately $34.13 from the sale.