Question 982962
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(3x+2y=c,9x=c)}}}


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/9 }}}

-
{{{3(c/9)+2y=c}}}
{{{c/3+2y=c}}}
{{{2y=c-c/3}}}
{{{y=(1/2)(c-c/3)}}}
{{{y=(1/2)(2/3)c}}}
{{{y=c/3}}}


Look at the two prices:
{{{x=c/9}}} and {{{y=c/3}}}
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((1/3)*NINE=highlight(3))}}}, <b>THREE ice cream cones</b>.


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