2 numbers that subtract to 21 and divide to 4
MathBot Answer:
The numbers are \(28\) and \(7\).
The difference between the numbers is \(21\), and their quotient is \(4\). This translates to the two equations: \[\begin{aligned}n_{1} - n_{2} &= 21\\\frac{n_{1}}{n_{2}} &= 4\\\end{aligned}\] Solving the second equation for \(n_{1}\) in terms of \(n_{2}\) produces the formula \(n_{1} = 4 n_{2}\). Substituting the formula for \(n_{1}\) into the first equation yields:\[\begin{gather*}4 n_{2} - n_{2} = 21\\3 n_{2} = 21\end{gather*}\] So, \(n_{2} = 7\). Substituting \(7\) for \(n_{2}\) in the first equation results in \(n_{1} - 7 = 21\), so \(n_{1} = 28\).