Answer:
The equations are:
[tex]4H + 3P = 13.75[/tex]
[tex]2H + 5P = 11.25[/tex]
[tex]Hotdog = 2.50[/tex]
[tex]Pretzel = 1.25[/tex]
Step-by-step explanation:
Let:
[tex]H = hot\ dog[/tex]
[tex]P =Pretzel[/tex]
For Tina:
[tex]4H + 3P = 13.75[/tex]
For Doug:
[tex]2H + 5P = 11.25[/tex]
Solving for the price of both items:
We have:
[tex]4H + 3P = 13.75[/tex] --- (1)
[tex]2H + 5P = 11.25[/tex] --- (2)
Multiply (2) by 2
2 * ([tex]2H + 5P = 11.25[/tex])
-------------------
[tex]4H + 10P = 22.50[/tex] --- (3)
Subtract (3) from (1)
[tex]4H + 3P = 13.75[/tex]
[tex]4H + 10P = 22.50[/tex]
----------------------
[tex]4H - 4H + 3P - 10P = 13.75 - 22.50[/tex]
[tex]3P - 10P = 13.75 - 22.50[/tex]
[tex]-7P = -8.75[/tex]
Solve for P
[tex]P = \frac{-8.75}{-7}[/tex]
[tex]P = 1.25[/tex]
Substitute 1.25 for P in (2)
[tex]2H + 5P = 11.25[/tex]
[tex]2H + 5 * 1.25 = 11.25[/tex]
[tex]2H + 6.25 = 11.25[/tex]
Collect Like Terms
[tex]2H = 11.25-6.25[/tex]
[tex]2H = 5[/tex]
Solve for H
[tex]H = \frac{5}{2}[/tex]
[tex]H = 2.50[/tex]
