Question

Jack, Jill, and Jon have 125 together . Jon has has 4 times what Jack has, and Jill has 5 more than Jack has. How much does each have.

Answer 1

Variables:

• Ja = Jack

,

• Ji = Jill

,

• Jo = Jon

Equations based on the information:

$Ja+Ji+Jo=125$$\begin{gathered} Jo=4\cdot Ja \\ or \\ Ja=\frac{Jo}{4} \end{gathered}$$\begin{gathered} Ja=5\cdot Ji\text{ } \\ or \\ Ji=\frac{Ja}{5} \end{gathered}$

Procedure

$\begin{gathered} Ja+Ji+Jo=125 \\ Ja+\frac{Ja}{5}+4\cdot Ja=125 \\ Ja(1+\frac{1}{5}+4)=125 \\ Ja=\frac{125}{(1+\frac{1}{5}+4)}\approx24 \end{gathered}$$Ji=\frac{24}{5}\approx4.8\approx5$$Jo=4\cdot24\approx96$

Answer: Jack = 24, Jill = 5, and Jon = 96