Answer:
311.6 cm
Step-by-step explanation:
To solve this problem, let's call:
k = Keith's height
n = nephew's height
Since the ratio is 15:7, we have
[tex]\frac{k}{n}=\frac{15}{7}\\k=\frac{15}{7}n[/tex] (1)
Then, Keith's height is increased by 16%, so the new height of Keith is
[tex]k'=k+0.16 = 1.16k[/tex] (2)
While the nephew's height is doubled:
[tex]n'=2n[/tex] (3)
We also know that Keith is now 34 cm taller than his nephew, so
[tex]k'=n'+34[/tex] (4)
Substituting (2) and (3) into (4), we get
[tex]1.16k=2n+34[/tex]
And substituting (1),
[tex]1.16\cdot \frac{15}{7}n=2n+34[/tex]
Solving for n,
[tex]2.49n=2n+34\\\\0.49n=34\\n=\frac{34}{0.49}=69.4[/tex]
So the current height of the nephew is:
[tex]n'=2n=2(69.4)=138.8 cm[/tex]
While Keith's current height is
[tex]k'=138.8+34=172.8 cm[/tex]
So their total current height is
[tex]k'+n'=172.8+138.8=311.6 cm[/tex]
