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Sagot :
EXPLANATION
Assuming that x represents the age of Ellie, y represents the age of Maisy and z represents the age of Zoe, we can apply the following relationships:
x + y + z = 50 (1)
x = 6 + y (2)
z = 2x (3)
We have a system of three equations with three variables, thus we can compute the system as follows:
[tex]\mathrm{Substitute\: }z=2x[/tex][tex]\begin{bmatrix}x=6+y \\ x+y+2x=50\end{bmatrix}[/tex][tex]Simplify\text{ }x+y+2x=50[/tex]Grouping like terms:
[tex]3x\text{ + y = 50}[/tex]Now, we have:
[tex]\begin{bmatrix}x=6+y \\ 3x+y=50\end{bmatrix}[/tex][tex]\mathrm{Substitute\: }x=6+y[/tex][tex]\begin{bmatrix}3\mleft(6+y\mright)+y=50\end{bmatrix}[/tex]Applying the distributive property:
[tex]\begin{bmatrix}18+4y=50\end{bmatrix}[/tex][tex]\mathrm{Subtract\: }18\mathrm{\: from\: both\: sides}[/tex][tex]18+4y-18=50-18[/tex][tex]Simplify\colon[/tex][tex]4y=32[/tex][tex]\mathrm{Divide\: both\: sides\: by\: }4[/tex][tex]\frac{4y}{4}=\frac{32}{4}[/tex][tex]Simplify\colon[/tex][tex]y=8[/tex][tex]\mathrm{For\: }x=6+y[/tex][tex]\mathrm{Substitute\: }y=8[/tex][tex]x=6+8[/tex][tex]Simplify\colon[/tex][tex]x=14[/tex][tex]\mathrm{For\: }z=2x[/tex][tex]\mathrm{Substitute\: }x=14,\: y=8[/tex][tex]z=2\cdot\: 14[/tex][tex]\mathrm{Simplify}[/tex][tex]z=28[/tex][tex]\mathrm{The\: solutions\: to\: the\: system\: of\: equations\: are\colon}[/tex][tex]x=14,\: z=28,\: y=8[/tex]In conclusion, the age of Zoe is 28 years old.
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