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14 votes
14 votes
15) Ellie is six years older than Maisy. Zoe istwice as old as Ellie. The sum of their ages is50. How old is Zoe?

User Eugene Trifonov
by
3.1k points

1 Answer

5 votes
5 votes

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:


\mathrm{Substitute\: }z=2x
\begin{bmatrix}x=6+y \\ x+y+2x=50\end{bmatrix}
Simplify\text{ }x+y+2x=50

Grouping like terms:


3x\text{ + y = 50}

Now, we have:


\begin{bmatrix}x=6+y \\ 3x+y=50\end{bmatrix}
\mathrm{Substitute\: }x=6+y
\begin{bmatrix}3\mleft(6+y\mright)+y=50\end{bmatrix}

Applying the distributive property:


\begin{bmatrix}18+4y=50\end{bmatrix}
\mathrm{Subtract\: }18\mathrm{\: from\: both\: sides}
18+4y-18=50-18
Simplify\colon
4y=32
\mathrm{Divide\: both\: sides\: by\: }4
(4y)/(4)=(32)/(4)
Simplify\colon
y=8
\mathrm{For\: }x=6+y
\mathrm{Substitute\: }y=8
x=6+8
Simplify\colon
x=14
\mathrm{For\: }z=2x
\mathrm{Substitute\: }x=14,\: y=8
z=2\cdot\: 14
\mathrm{Simplify}
z=28
\mathrm{The\: solutions\: to\: the\: system\: of\: equations\: are\colon}
x=14,\: z=28,\: y=8

In conclusion, the age of Zoe is 28 years old.

User Quizac
by
2.8k points
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