For Each problem set up a legend set up two equations write answers in full sentences( solve using elimination

Castle and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Castle sold 6 apple pies and 4 lemon for a total of 80. Gabriella sold 6 apple pies and 5 lemon pies for a total of 94. What is the cost each of one apple pie and one lemon pie?

6a + 4l = 80

6a + 5l = 94
subtract them: l = 14
plug back into the first to get a

To solve this problem using elimination, we need to set up a system of equations using the given information.

Let's assume the cost of one apple pie is 'a' and the cost of one lemon meringue pie is 'l'.

Castle sold 6 apple pies and 4 lemon meringue pies for a total of $80, so we can set up the first equation:

6a + 4l = 80 --(1)

Gabriella sold 6 apple pies and 5 lemon meringue pies for a total of $94, so we can set up the second equation:

6a + 5l = 94 --(2)

Now, we can solve this system of equations using elimination.

To eliminate 'a', we can multiply equation (1) by 6 and equation (2) by 4. This will result in both equations having the same coefficient for 'a'.

6 * (6a + 4l) = 6 * 80
4 * (6a + 5l) = 4 * 94

Simplifying, we get:

36a + 24l = 480 --(3)
24a + 20l = 376 --(4)

Now, we can eliminate 'a' by subtracting equation (4) from equation (3):

(36a + 24l) - (24a + 20l) = 480 - 376

Simplifying, we get:

12a + 4l = 104 --(5)

Now we have two equations, (5) and (2), with the same variables (a and l).

12a + 4l = 104 --(5)
6a + 5l = 94 --(2)

To eliminate 'l', we can multiply equation (5) by 5 and equation (2) by 4. This will result in both equations having the same coefficient for 'l'.

5 * (12a + 4l) = 5 * 104
4 * (6a + 5l) = 4 * 94

Simplifying, we get:

60a + 20l = 520 --(6)
24a + 20l = 376 --(7)

Now, we can eliminate 'l' by subtracting equation (7) from equation (6):

(60a + 20l) - (24a + 20l) = 520 - 376

Simplifying, we get:

36a = 144

Dividing both sides by 36, we find:

a = 4

Now, we can substitute the value of 'a' back into equation (2) to solve for 'l':

6(4) + 5l = 94

Simplifying, we get:

24 + 5l = 94

Subtracting 24 from both sides, we have:

5l = 70

Dividing both sides by 5, we find:

l = 14

Therefore, the cost of one apple pie is $4 and the cost of one lemon meringue pie is $14.