Ryan and Ming are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and pacakges of gingerbread cookie dough. Ryan sold 13 packages of white chocolate chip cookie dough and 14 packages of gingerbread cookie dough for a total of $244. Ming sold 6 packages of white chocolate chip cookie dough and 4 packages of gingerbread cookie dough for a total of $88. What is the cost each of one package of white chocolate chip cookie dough and one package of gingerbread cookie dough?

Question

anonymous · Answer

13x+14y=244 and 6x+4y=88
@phi

anonymous · Answer

the second equation oes to 3x+2y=44

anonymous · Answer

we have to figure out how to get the number before x the same on both equations right?

anonymous · Answer

can't we do that easier with y though?

phi · Answer

yes, pick the easier one

anonymous · Answer

hmm I'm trying to think of the least common denominator (that's what it's called right?)

anonymous · Answer

can't we just do 2 times 7 to get the y in the second equation to 14 as well?

anonymous · Answer

or do you have to do something to the first equation too?

anonymous · Answer

I hope I'm making sense haha

phi · Answer

least common multiple 
yes 14 is what you want

anonymous · Answer

okay cool

anonymous · Answer

21x+14y=308

phi · Answer

technically you could multiply the top equation by 1 if you want. (but that is being a bit silly)

phi · Answer

ok, now you have
13x+14y=244
21x+14y=308

anonymous · Answer

x=8 ?

anonymous · Answer

y=10?

phi · Answer

yes
if we subtract bottom from top (though I would do it the other way round) , we get
-8x = -64
x = -64/-8 = 8

anonymous · Answer

great :) thank you for all your help!!

phi · Answer

yw