Micaela and Aliyah are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and chocolate marble cheesecakes. Micaela sold 8 pecan cheesecakes and 10 chocolate marble cheesecakes for a total of $240. Aliyah sold 10 pecan cheesecakes and 8 chocolate marble cheesecakes for a total of $212. Find the cost of one pecan cheesecake and one chocolate marble cheesecake.

Question

anonymous · Answer

8x+10y=240      10x+7y=212 
@phi

phi · Answer

you can simplify the first equation

anonymous · Answer

4x+5y=120

phi · Answer

ok, now you have
4x+5y=120
10x+7y=212 

what's a "least common denominator" of 4 and 10 ?

anonymous · Answer

is it 2?

phi · Answer

you can practice that later.  but  4*5 is 20  and 2*10 is 20

phi · Answer

the idea is to make the number in front of the x the same in both equations
(I picked x because the numbers look a tiny bit simpler than for y)

anonymous · Answer

ok so does that make the number infront of x 20?

phi · Answer

if you multiply the top equation by 5
and the bottom by 2
can you do that ?

anonymous · Answer

20x+25y=600 and 20x+14y=424

phi · Answer

ok,

btw, the problem says
Aliyah sold 10 pecan cheesecakes and 8 chocolate marble cheesecakes for a total of $212
but you are using 10x+7y=212

??

anonymous · Answer

oh god, I keep hitting the wrong key hahaha I meant 8!!

anonymous · Answer

I wrote it like that too, jeez I must be slow today

anonymous · Answer

let me fix this then okay. so 20x+16y=424 then

phi · Answer

ok.  now you have
20x+25y=600 
 20x+16y=424

any ideas?

anonymous · Answer

do you subtract the bottom equation from the top?

phi · Answer

either way,  but it's slightly nicer to subtract the bottom from the top

anonymous · Answer

ok so the 20x-20x cancels out and then 25y-16y=9 and 600-424=176

phi · Answer

25y-16y=9 

not just 9.  it is 9y

anonymous · Answer

yes 9y=176

anonymous · Answer

176 divided by 9? right? 19.555556 it says

phi · Answer

we are going to get an fraction or decimal in the answer.
(It was nicer if we could use 7 instead of 8)

anonymous · Answer

haha true

anonymous · Answer

so y=19.5 and x=5.625?

phi · Answer

x and y are dollars and cents

anonymous · Answer

ok but that's right?

phi · Answer

If you don't use fractions when solving for x then you should use y with as many decimals as your calculator allows (do not round)

anonymous · Answer

well it was 19.5555556 and 5.625 I'm pretty sure

phi · Answer

you should get x= 50/9 = 5.5555...

anonymous · Answer

ahhh I must've just clicked something wrong.

phi · Answer

and at the end, round to the nearest cent:  19.56 and 5.56

anonymous · Answer

ok that makes sense. thank you so much :) I just have one question left that I've started. I'll make a new post