document.write( "Question 951824: Ramona bought 5 hamburgers and 3 pizzas for $167.75. If she had bought 4 hamburgers and 4 pizzas, then she would have paid $193. How much did Ramona pay for each hamburger and each pizza?\r
\n" ); document.write( "\n" ); document.write( "I have tried using ratio and proportion so as not to confuse myself but i just cant figure this out. \n" ); document.write( "

Algebra.Com's Answer #581333 by KMST(5328) $\"\"$ $\"About$

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Try using systems of linear equations.
\n" ); document.write( "You have two variables to be named/defined:
\n" ); document.write( " $\"x\"$ = price (in $) for a hamburger, and
\n" ); document.write( " $\"y\"$ = price (in $) for a pizza.
\n" ); document.write( "(You could also break with the tradition of using $\"x\"$ and $\"y\"$ ,
\n" ); document.write( "and use $\"H\"$ for the price of a hamburger and $\"P\"$ for the price of a pizza).
\n" ); document.write( "\"Ramona bought 5 hamburgers and 3 pizzas for $167.75\" translates as
\n" ); document.write( " $\"5x%2B3y=167.75\"$ .
\n" ); document.write( "\"If she had bought 4 hamburgers and 4 pizzas, then she would have paid $193\" translates as
\n" ); document.write( " $\"4x%2B4y=193\"$ .
\n" ); document.write( "Your system of linear equations is
\n" ); document.write( " $\"system%285x%2B3y=167.75%2C4x%2B4y=193%29\"$ .
\n" ); document.write( "There are many ways to go about solving it.
\n" ); document.write( "You could solve it \"by substitution\" or \"by elimination\".
\n" ); document.write( "One way to solve it \"by substitution\", would be
\n" ); document.write( "to solve $\"4x%2B4y=193\"$ for $\"y\"$ to get an equation that looks like $\"y=some\"$ $\"expression\"$ ;
\n" ); document.write( "substitute the expression you find for $\"y\"$ in the other equation:
\n" ); document.write( "solve the resulting equation for $\"x\"$ ,
\n" ); document.write( "and plug the $\"x\"$ value found into the $\"y=some\"$ $\"expression\"$ equation,
\n" ); document.write( "to find the value for $\"y\"$ .
\n" ); document.write( "It would go like this:
\n" ); document.write( " $\"4x%2B4y=193\"$ --> $\"4y=193-4x\"$ --> $\"%281%2F4%29%284y%29=%281%2F4%29%28193-4x%29\"$ --> $\"y=%281%2F4%29%28193%29-%281%2F4%29%284x%29\"$ --> $\"y=48.25-x\"$
\n" ); document.write( " $\"5x%2B3y=167.75\"$ --> $\"5x%2B3%2848.25-x%29=167.75\"$ --> $\"5x%2B3%2A48.25-3x=167.75\"$ --> $\"5x%2B144.75-3x=167.75\"$ --> $\"2x%2B144.75=167.75\"$ --> $\"2x=167.75-144.75\"$ --> $\"2x=23\"$ --> $\"x=23%2F2\"$ --> $\"highlight%28x=11.50%29\"$
\n" ); document.write( " $\"y=48.25-x\"$ --> $\"y=48.25-11.50\"$ --> $\"highlight%28y=36.75%29\"$ \n" ); document.write( "

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