+0

# age

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1293
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Bill is now 100% older then his younger sister Rebecca

In 8 years he will be 20% older

How old is Rebecca now?

Feb 12, 2016

#1
+5

Rebecca's age = x    Bill's age = 2x     2x + 8 = 1.2(x+8)

.8x = 1.6

x = 1.6/.8=2    Bill is 4      Rebecca is 2

Feb 12, 2016

#1
+5

Rebecca's age = x    Bill's age = 2x     2x + 8 = 1.2(x+8)

.8x = 1.6

x = 1.6/.8=2    Bill is 4      Rebecca is 2

Guest Feb 12, 2016
#2
+5

100% older means twice as old

20%  older means 6/5 as old

Let  Rebecca's current age  = x      so....Bill's = 2x

In 8 years we have........his age =  6/5 her age

2x + 8 =  (6/5) [ x + 8]   simplify

2x + 8 = (6/5)x + 48/5

2x + 8 = (6/5)x + 48/5      subtract 8, (6/5)x from both sides

2x - (6/5)x  = 48/5 - 8

(4/5)x  = 8/5   multiply through by 5

4x  = 8      divide both sides by 4

x  = 2       this is Rebecca's current age.......so Bill = 2x  =4

And...in 8 years, Rebecca will be 10 and Bill will be 12    .....and   12 is 6/5 of 10  →  20% more than 10   Feb 12, 2016
edited by CPhill  Feb 12, 2016
edited by CPhill  Feb 12, 2016