Siblings

Algebra Level 2

Hannah is 7 years older than Tim was 2 years ago. If Tim is half of Hannah's age at present, then how old is Hannah now?

16 6 8 10

Colton Haefeker by Colton Haefeker , 21, USA

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2 solutions

Chew-Seong Cheong
Apr 14, 2016

Let Hannah and Tim be x x and y y years old now respectively. Then,

{ x = y − 2 + 7 = y + 5 . . . ( 1 ) y = x 2 . . . ( 2 ) \begin{cases} x=y-2+7=y+5 &... (1) \\ y=\dfrac{x}{2} &... (2) \end{cases}

⇒ x = x 2 + 5 x 2 = 5 ⇒ x = 10 \begin{aligned} \Rightarrow x & =\frac {x} {2} +5 \\ \frac {x} {2} & =5\\ \Rightarrow x & =\boxed{10} \end{aligned}

1 Helpful 0 Interesting 0 Brilliant 1 Confused
Shane Lorenzen
Apr 14, 2016

Hannah is 5 years older than Tim, so 10 -5=5, 5 is half of 10.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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