SOLUTION: George has just enough money to buy 3 chocolate bars and 2 ice cream cones. For the same amount of money, he could buy exactly 9 chocolate bars. For the same amount of money, how

Algebra ->  Finance -> SOLUTION: George has just enough money to buy 3 chocolate bars and 2 ice cream cones. For the same amount of money, he could buy exactly 9 chocolate bars. For the same amount of money, how       Log On


   

Question 982962: George has just enough money to buy 3 chocolate bars and 2 ice cream cones. For the same amount of money, he could buy exactly 9 chocolate bars. For the same amount of money, how many ice cream cones could George buy?
On my part, I have gotten 3 cones as my answer.
This is How I Did It:
3x+2y=z
9x=z
That means 6x=2y So I did this proportion:
6x/2y=9x/? ---> 6x?=18yx ----> Divide by 6x
?= 3y I don't think thing is correct.
Show me your way!
Found 2 solutions by Fombitz, josgarithmetic:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3x%2B2y=z
9x=z
Substituting,
3x%2B2y=9x
2y=6x
So then multiplying both sides by 3%2F2,
3x=9y=z
So you can buy 3 ice cream cones for the same price of 9 chocolate bars.
Well done.

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Price & Cost type problem. You want to find the prices of each item. Both are unknown, and the costs are also unknown.

x, price for chocolate bar
y, price for ice cream cone
c, the cost of whatever he purchases, the same in all cases; how much money he has

system%283x%2B2y=c%2C9x=c%29

Two equations but three unknown variables. This problem would have several solutions. ?
Keep going, trying to solve x and y in terms of c.


x=c%2F9+
-
3%28c%2F9%29%2B2y=c
c%2F3%2B2y=c
2y=c-c%2F3
y=%281%2F2%29%28c-c%2F3%29
y=%281%2F2%29%282%2F3%29c
y=c%2F3

Look at the two prices:
x=c%2F9 and y=c%2F3
You can see the ratio between the two prices.
The chocolate bar is cheaper than the icecream cone.
The ice cream cone is three times the price of the chocolate bar.
NINE chocolate bars, same amount of money, only highlight%28%281%2F3%29%2ANINE=highlight%283%29%29, THREE ice cream cones.

We do not really need the actual prices nor the actual cost c.
We really just needed their ratio of x and y for this problem