Answer:
[tex]\$1.09[/tex]
Step-by-step explanation:
All the costs mentioned here are before tax
Let cost of junior bacon cheese burger be [tex]x[/tex]
Cost of large fries be [tex]y[/tex]
Heather's order cost 12.50
[tex]6x+4y=12.5\quad\ldots (i)[/tex]
Sarah's order cost 13.70
[tex]3x+7y=13.7\quad\ldots (ii)[/tex]
Multiply [tex](ii)[/tex] by [tex]2[/tex]
[tex]6x+4y=12.5[/tex]
[tex]6x+14y=27.4[/tex]
Subtracting the equations we get
[tex]-10y=-14.9\\\Rightarrow y=\dfrac{14.9}{10}\\\Rightarrow y=1.49[/tex]
Cost of large fries is [tex]\$1.49[/tex]
[tex]6x+4y=12.5\\\Rightarrow x=\dfrac{12.5-4y}{6}\\\Rightarrow x=\dfrac{12.5-4\times 1.49}{6}\\\Rightarrow x=1.09[/tex]
Cost of junior bacon cheeseburger before tax is [tex]\$1.09[/tex].
