Question

Carlos and Kathryn are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Carlos sold 14 apple pies and 6 lemon meringue pies for a total of $266. Kathryn sold 6 apple pies and 10 lemon meringue pies for a total of $218. Find the cost each of one apple pie and one lemon meringue pie.

Answer 1

14x+6y=266 and 6x+10y=218

Answer 2

7x+3y=133 and 2x+5y=109 right?

Answer 3

I'm not sure what to do next though.

Answer 4

those look good.
I would simplify both of them by divide both sides by 2

Answer 5

7x+3y=133
2x+5y=109

if you make the numbers in front of the y (for example) the same , we can solve
I would multiply the top equation (both sides) by 5
and the bottom by 3
what do you get for the two new equations?

Answer 6

notice I wanted the greatest common factor (like finding a "common denominator")
of 3 and 5. i.e. 15

Answer 7

35x+15y and 6x+15y?

Answer 8

except you have to write the *entire* equation. (both sides)

Answer 9

but is 35x+15y right?

Answer 10

yes, you did the left half of each equation correctly

Answer 11

okay so you multiply 133 by 5 and 109 by 3?

Answer 12

yes

Answer 13

ok so then we have 35x+15y=665 and 6x+15y=327

Answer 14

35x+15y=665
6x+15y=327

now subtract the bottom equation from the top equation
or if you like, multiply the bottom equation by -1 (both sides), then add the equations

Answer 15

I notice a small mistake
you started with
6x+10y=218

when you simplify by dividing both sides by 2 you should get
3x + 5y = 109
(you wrote down 2x ).

Answer 16

I accidentally wrote 2 instead of 3 haha

Answer 17

I noticed that too

Answer 18

I'm kinda stuck on these last equations though.

Answer 19

that changes the equations to
35x+15y=665
9x+15y=327

Answer 20

35-9=26 and then the 15 cancels out and 665-327=338

Answer 21

yes, that is the correct idea, but leave in the letter
you are doing
35x -9x + 15y - 15y = 665-327

Answer 22

35 x's take away 9 x's leaves 26 x's
i.e.
35x -9x + 15y - 15y = 665-327
simplifies to
26x = 338

Answer 23

now divide both sides by 26

Answer 24

like 338 divided by 26? that's 13

Answer 25

yes. you are doing
\[ \frac{26x}{26} = \frac{338}{26} \]
now simplify both sides

Answer 26

on the left side 26/26 is 1, and 1*x is just x
on the right side you get 13
so after simplifying you get
x= 13

Answer 27

perfect and then y=14 :) thank you

Answer 28

I have 2 other questions just like this, could you help me again? I'm starting to get the hang of it haha

Answer 29

ok, but please make a new post.

Answer 30

gotcha :)