Respuesta :
Let [tex] z, a, e [/tex] be the ages of Zelda, Adam and Elliot, respectively.
Let's translate the given information into equations: Zelda is seven times as old as Adam means that [tex] z = 7a [/tex]
Adam is three years younger than Elliot means [tex] a = e-3 [/tex]
Next year, Zelda will be four times as old as Elliot means [tex] z+1 = 4(e+1) [/tex]
So, you have the system
[tex] \begin{cases} z = 7a\\a = e-3\\z+1 = 4(e+1)\end{cases} [/tex]
Use the first equation to express z in terms of a: the last two equations become
[tex] \begin{cases} a = e-3\\7a+1 = 4(e+1)\end{cases} [/tex]
Use the first equation to express a in terms of e: the last equation becomes
[tex] 7(e-3)+1=4(e+1) \iff 7e-21+1=4e+4 \iff 3e = 24 \iff e=8 [/tex]
So, Elliot is 8 years old. Adam is three years younger, so he is 5 years old. Zelda is seven times as old as Adam, so she is 35 years old.
