# The sum of Robin's age and Bruno's age is 45.Seven years ago,Robin was 16 years more than one half as old as bruno was then.How old was Bruno? :)

1
by Dragonfury1455

• Brainly User
2016-02-09T18:03:40+08:00

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Sum of present ages:
x + y = 45
y = 45 - x

Present ages:
Robin: x
Bruno: 45 - x

Ages seven years ago:
Robin:  x - 7
Bruno: 45 - 7 - x  or   38 - x

Equation:

x - 7 = 16 + ¹/₂ (38 - x)

x - 7 = 16 + 19 - x/2

x - 7 = 35 - x/2

(2) (x-7) = (35-x/2) (2)

2x - 14 = 70 - x

2x + x = 70 + 14

3x = 84

3x/3 = 84/3

x = 28

Present ages:  Plug-in 28 to x
Robin:  28 years old
Bruno:  45 - 28 = 17 years old

Ages seven years ago:
Robin: 28 - 7 = 21 years old
Bruno: 17 - 7 = 10 years old

ANSWER:  Bruno was 10 years old (seven years ago).

Check
Sum of their ages at present is 45.
28 + 17 = 45
45 = 45   (True)

Comparison of ages seven years ago:
21 = ¹/₂ (10) + 16
21 = 5 + 16
21 = 21   (True)