Question

Some time ago , Keith's height and his nephew's height were at a ratio of 15:7. Then, Keiths height increased by 16% and his nephew,s height doubled. Keith is now 34 cm taller than his nephew, what is their total current height

Answer 1

The answer is below

Explanation:

The ratio of Keith's height and his nephew's height is 15:7. Let keith height be x cm and his nephews height be y cm.

`(x)/(y)=(15)/(7) \\x=(15)/(7)y`

Keiths height increased by 16% , therefore Keith new height is (100% + 16%) × x = 1.16x

The nephew height is doubled, therefore his new height is 2y.

Given that Keith is now 34 cm taller than his nephew

1.16x = 2y + 34

but x = (15/7)y

`1.16((15)/(7) )y=2y+34\\\\(87)/(35) y=2y+34\\\\(87)/(35) y-2y=34\\\\(17)/(35)y=34\\ \\y=(34*35)/(17)\\ \\y=70\ cm`

The nephews new height = 2y = 2(70) = 140 cm

Keith new height = 2y + 34 = 140 + 34 = 174 cm

Their total current height = 140 cm + 174 cm = 314 cm