Question

finally, lets solve the word problem below by creating and solving a system of equations. on monday, jack bought 2 burgers and 3 fries for $11.25. on tuesday, he bought 7 burgers and 5 fries for $32.50. find the price of each item. solution: a burger costs ____ and a fry costs ____.

Explanation:

Step1: Define variables

Let $x$ be the price of a burger and $y$ be the price of fries. Then we have the following system of equations based on the given information:
$2x + 3y=11.25$ (Monday's purchase)
$7x + 5y=32.50$ (Tuesday's purchase)

Step2: Multiply equations to eliminate a variable

Multiply the first - equation by 5 and the second - equation by 3:
$5(2x + 3y)=5\times11.25\Rightarrow10x + 15y = 56.25$
$3(7x + 5y)=3\times32.50\Rightarrow21x+15y = 97.5$

Step3: Subtract equations

Subtract the first new - equation from the second new - equation:
$(21x + 15y)-(10x + 15y)=97.5 - 56.25$
$21x+15y - 10x - 15y=41.25$
$11x=41.25$
$x = 3.75$

Step4: Find the value of $y$

Substitute $x = 3.75$ into the first original equation $2x+3y = 11.25$:
$2\times3.75+3y=11.25$
$7.5+3y=11.25$
$3y=11.25 - 7.5$
$3y = 3.75$
$y = 1.25$

Answer:

A burger costs $\$3.75$ and a fry costs $\$1.25$