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=(Jo)/(4) \end{gathered}`
`\begin{gathered} Ja=5\cdot Ji\text{ } \\ or \\ Ji=(Ja)/(5) \end{gathered}`

Procedure

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

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