Samuel made a total of 91 pies and puffs.1/3 of the pies and 16 puffs were sold.There was an equal number of puffs and pies left. How many puffs did Samuel make?
If there were p puffs, then
p-16 = 2/3 (91-p)
number of puffs --- x
number of pies --- y
x + y = 91 -------> y = 91-x
pies sold: 1/3 y, leaving (2/3)y
puffs sold: 16, leaving x - 16
these are supposed to be equal
(2/3)y = x - 16
2y = 3x - 48
y = (3x-48)/2 , sub in y = 91-x
91-x = (3x-48)/2
182 - 2x = 3x - 48
-5x = -230
x = 46 , then y = 91-46 = 45
state your conclusion.
Let's assume the number of pies Samuel made as 'p' and the number of puffs as 'q'.
According to the given information, Samuel made a total of 91 pies and puffs. So, we can write the equation as:
p + q = 91 (Equation 1)
It is given that 1/3 of the pies and 16 puffs were sold. So, the number of pies sold would be (1/3) * p, and the number of puffs sold would be 16. It is also given that there was an equal number of puffs and pies left. So, we can write the equation as:
p - (1/3) * p = q - 16 (Equation 2)
Simplifying Equation 1, we get:
p = 91 - q
Substituting the value of p in Equation 2, we get:
(91 - q) - (1/3) * (91 - q) = q - 16
Now, we can solve this equation to find the value of q.
First, let's simplify the equation by distributing:
91 - q - (1/3) * 91 + (1/3) * q = q - 16
Now, we can combine like terms:
91 - q - (1/3) * 91 + (1/3) * q - q = -16
Simplifying further, we get:
91 - (1/3) * 91 - q + (1/3) * q - q = -16
Now, combining like terms again:
91 - (1/3) * 91 - (5/3) * q = -16
To isolate 'q', we can simplify further:
[91 - (1/3) * 91] + (5/3) * q = -16
Simplifying the terms inside the square brackets:
[(2/3) * 91] + (5/3) * q = -16
Now, let's simplify the terms inside the square brackets:
(2/3) * 91 = (2/3) * 273 = 182
Substituting the value of (2/3) * 91 = 182 in the equation, we get:
182 + (5/3) * q = -16
Now, let's isolate 'q' by subtracting 182 from both sides of the equation:
(5/3) * q = -16 - 182
(5/3) * q = -198
To solve for 'q', we need to multiply both sides of the equation by (3/5):
q = (-198) * (3/5)
q = (-198 * 3)/5
q = -594/5
q = -118.8
Since we cannot have a fraction of a puff, the number of puffs Samuel made cannot be a decimal or negative. Therefore, Samuel did not make any puffs because the given information is not feasible.
To solve this problem, let's break it down step by step:
Step 1: Determine the total number of pies and puffs that Samuel made.
- We are given that Samuel made a total of 91 pies and puffs.
Step 2: Calculate the number of pies and puffs sold.
- It is stated that 1/3 of the pies and 16 puffs were sold.
- To find the number of pies sold, we can calculate 1/3 of the total number of pies: (1/3) * total number of pies.
- Since the problem does not provide the exact number of pies, we'll represent it as x.
- So, the number of pies sold would be (1/3) * x.
- The number of puffs sold is given as 16.
Step 3: Calculate the number of pies and puffs left.
- It is mentioned in the problem that there was an equal number of puffs and pies left.
- Let's represent the number of pies and puffs left as y, since we don't know their exact values.
- So, the number of pies left is y, and the number of puffs left is also y.
Step 4: Set up an equation to solve for the unknowns.
- The total number of pies and puffs made is given as 91.
- We know that the number of pies sold is (1/3) * x.
- The number of puffs sold is 16.
- The number of pies and puffs left is y for both.
- Putting all these values together, we can set up the equation:
(1/3) * x + 16 + 2y = 91.
Step 5: Solve the equation to find the value of y.
- Rearranging the equation, we have:
(1/3) * x + 2y = 91 - 16.
(1/3) * x + 2y = 75.
- Since the problem states that the number of pies left is equal to the number of puffs left, we can substitute y for both variables:
(1/3) * x + 2y = 75 becomes (1/3) * x + 2y = 75.
- To simplify the equation, we'll multiply both sides by 3 to eliminate the fraction:
x + 6y = 225.
Step 6: Use the given information to solve the equation.
- The problem does not provide any specific information to calculate x, but it asks for the number of puffs Samuel made (y).
- Therefore, we can assume x is a variable representing the number of pies.
- Let's solve the equation for y:
x + 6y = 225.
Given that the number of pies and puffs left is the same, we can substitute y for both variables:
x + 6 (y) = 225.
x + 6y = 225.
- Since the equation does not provide the value of x (number of pies), we cannot solve it to find the exact value of y (number of puffs).
- We can, however, express the solution in terms of y.
- Therefore, the number of puffs Samuel made cannot be determined with the given information.