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MrRoyal

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]

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