SOLUTION: 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 ea

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?
I have tried using ratio and proportion so as not to confuse myself but i just cant figure this out.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Try using systems of linear equations.
You have two variables to be named/defined:
= price (in $) for a hamburger, and
= price (in $) for a pizza.
(You could also break with the tradition of using and ,
and use for the price of a hamburger and for the price of a pizza).
"Ramona bought 5 hamburgers and 3 pizzas for $167.75" translates as
.
"If she had bought 4 hamburgers and 4 pizzas, then she would have paid $193" translates as
.
Your system of linear equations is
.
There are many ways to go about solving it.
You could solve it "by substitution" or "by elimination".
One way to solve it "by substitution", would be
to solve for to get an equation that looks like ;
substitute the expression you find for in the other equation:
solve the resulting equation for ,
and plug the value found into the equation,
to find the value for .
It would go like this:
-->-->-->-->
-->-->-->-->-->-->-->-->
-->-->
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