Steve and Belinda are selling pies for a school fundraiser. Customers can buy apple pies and cherry pies.
John sold 3 apple pies and 9 cherry pies for a total of $183.
Belinda sold 6 apple pies and 13 cherry pies for a total of $276.
What is the cost each of one apple pies and cherry pies ?
3 a + 9 c = 183
6 a + 13 c = 276
multiply first equation by 2
6 a + 18 c = 366
6 a + 13 c = 276
---------------- subtract
5 c = 90
c = 18
etc
To find the cost of one apple pie and one cherry pie, we can set up a system of equations using the given information.
Let x be the cost of one apple pie.
Let y be the cost of one cherry pie.
From John's sales:
3x + 9y = 183...........(Equation 1)
From Belinda's sales:
6x + 13y = 276..........(Equation 2)
We now have a system of two equations. To solve this system, we can use a method called substitution or elimination.
Let's use the method of elimination to solve this system of equations.
First, let's multiply Equation 1 by 2 and Equation 2 by 3 to make the coefficients of x in both equations the same:
6x + 18y = 366..........(Equation 3) [2 * Equation 1]
18x + 39y = 828..........(Equation 4) [3 * Equation 2]
Now, let's subtract Equation 3 from Equation 4 to eliminate x:
(18x + 39y) - (6x + 18y) = 828 - 366
12x + 21y = 462
Next, let's divide both sides of this equation by 3 to simplify it:
(12x + 21y)/3 = 462/3
4x + 7y = 154.............(Equation 5)
Now, we have a simplified equation with coefficients that are easy to work with. We can use this equation in combination with Equation 1 to solve for the values of x and y.
Let's multiply Equation 1 by 4 to make the coefficients of x in both equations the same:
12x + 36y = 732..........(Equation 6) [4 * Equation 1]
Now, let's subtract Equation 6 from Equation 5 to eliminate x:
(4x + 7y) - (12x + 36y) = 154 - 732
-8x - 29y = -578
Let's divide both sides of this equation by -1 to simplify it further:
(-8x - 29y)/-1 = -578/-1
8x + 29y = 578..................(Equation 7)
Now, we have a new equation (Equation 7) with both positive coefficients. We can use this equation in combination with Equation 6 to solve for the values of x and y.
Let's add Equation 7 and Equation 6:
(8x + 29y) + (12x + 36y) = 578 + 732
20x + 65y = 1310
Next, let's divide both sides of this equation by 5 to simplify it:
(20x + 65y)/5 = 1310/5
4x + 13y = 262
We now have a new equation (Equation 8). Let's solve this equation by subtracting Equation 5 from Equation 8:
(4x + 13y) - (4x + 7y) = 262 - 154
13y - 7y = 108
6y = 108
Now, let's solve for y by dividing both sides of this equation by 6:
y = 108/6
y = 18
We have found the value of y, which is the cost of one cherry pie. The cost of one cherry pie is $18.
To find the value of x, let's substitute the value of y back into either Equation 1 or Equation 2. Let's use Equation 1:
3x + 9y = 183
3x + 9 * 18 = 183
3x + 162 = 183
3x = 183 - 162
3x = 21
Now, let's solve for x by dividing both sides of this equation by 3:
x = 21/3
x = 7
We have found the value of x, which is the cost of one apple pie. The cost of one apple pie is $7.
Therefore, the cost of one apple pie is $7 and the cost of one cherry pie is $18.