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# Mr. Hart owns a small horse ranch. He also raises dogs on the ranch to help with the horses.Mr. Hart has a total budget of $\ 30,000$ to buy horses and dogs for the ranch. How many horses and dogs can Mr. Hart buy for his ranch if the relationship stays the same? Explain your reasoning. Show your work.

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Using the values from the tables for the relationship of horses and dogs, determine the number of dogs and horses that would fit the total budget of Mr. Hart.

Use ordered pairs $(2,8)$; $(3,11)$; $(4,14)$ and $(5,17)$ to determine the cost of buying dogs and horses. Use the equations, $c = 1,500h + 2,000$ and $b = 500d + 500$.

$\begin{gather*} c = 1,500h + 2,000 = 1,500(8) + 2,000 = 14,000\\ b = 500d + 500 = 500(2) + 500 = 1,500\\ 14,000 + 1,500 = \textbf{15,500} \end{gather*}$

$\begin{gather*} c = 1,500h + 2,000 = 1,500(11) + 2,000 = 18,500\\ b = 500d + 500 = 500(3) + 500 = 2,000 18,500 + 2,000 = \textbf{20,500} \end{gather*}$

$\begin{gather*} c = 1,500h + 2,000 = 1,500(14) + 2,000 = 23,000\\ b = 500d + 500 = 500(4) + 500 = 2,500 23,000 + 2,500 = \textbf{25,500} \end{gather*}$

$\begin{gather*} c = 1,500h + 2,000 = 1,500(17) + 2,000 = 27,500\\ b = 500d + 500 = 500(5) + 500 = 3,000 27,500 + 3,000 = \textbf{30,500} \end{gather*}$

The number of dogs and horses that would fit the total budget of Mr. Hart are $\textbf{4 dogs and 14 horses}$ making the relationship stay the same.

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