Question

P and q are two numbers such that p > q

Answer 1

The ratio p:9 is equal to 50:9 = $\frac{50}{9}$.

System of Linear Equations

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

For solving this equation, firstly, rewrite the information given:

                                          $\frac{p-5}{q-5}=\frac{9}{1} \;(1)\\ \\\frac{p+20}{q+20}=\frac{7}{3} \;(2)$

From equation 1, you have:

                                        $p-5=9q-45\\ \\ p=9q-40$

And from equation 2, you have:

                                  $3*(p+20)=7*(q+20)\\ \\ 3p+60=7q+140$

Now, substitute p=9q-40 in 3p+60=7q+140

                                 $3p+60=7q+140\\ \\3*(9q-40)=7q+140\\ \\ 27q-120=7q+140\\ \\ 20q=20\\ \\ q=10$

If q=10 for p=9q-40,  you will have:

                                $p=9q-40\\ \\ p=9*10-40\\ \\ p=90-40\\ \\ p=50$

Therefore, the ratio  $\frac{p}{9}$  is equal to $\frac{50}{9}$.

Learn more about the system of equations here:

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