Question

Keith's height and his nephews height was at a ratio of 15:7 then, keith's Height increased by 16% and his nephews height doubled. If Keith is now 34cm taller than his nephew, what is their total current height?

Answer 1

311.6 cm

Explanation:

To solve this problem, let's call:

k = Keith's height

n = nephew's height

Since the ratio is 15:7, we have

`(k)/(n)=(15)/(7)\\k=(15)/(7)n` (1)

Then, Keith's height is increased by 16%, so the new height of Keith is

`k'=k+0.16 = 1.16k` (2)

While the nephew's height is doubled:

`n'=2n` (3)

We also know that Keith is now 34 cm taller than his nephew, so

`k'=n'+34` (4)

Substituting (2) and (3) into (4), we get

`1.16k=2n+34`

And substituting (1),

`1.16\cdot (15)/(7)n=2n+34`

Solving for n,

`2.49n=2n+34\\\\0.49n=34\\n=(34)/(0.49)=69.4`

So the current height of the nephew is:

`n'=2n=2(69.4)=138.8 cm`

While Keith's current height is

`k'=138.8+34=172.8 cm`

So their total current height is

`k'+n'=172.8+138.8=311.6 cm`