SOLUTION: a girl is currently 5 years older than her younger brother and 3 years younger than her older brother. 2 years from the current time, the product of the ages of the brothers will b

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Question 1094915: a girl is currently 5 years older than her younger brother and 3 years younger than her older brother. 2 years from the current time, the product of the ages of the brothers will be 12 times the age of the girl. what is the current age of the oldest brother
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+-+2+ = the girl's age now
Let +b+-+2+ = her younger brother's age now
Let +c+-+2+ = her older brother's age now
( I did this to make the 3rd equation simpler )
----------------------------------------
With 3 unknowns, I need 3 equations
(1) +a+-+2+=+b+-+2+%2B+5+
(2) +a+-+2+=+c+-+2+-+3+
(3) +%28+b+-+2+%2B+2+%29%2A%28+c+-+2+%2B+2+%29+=+12%2A%28+a+-+2+%2B+2+%29+
--------------------------------------
(3) +b%2Ac+=+12a+
and
(1) +a+-+2+=+b+%2B+3+
(1) +a+-+b+=+5+
----------------------
(2) +a+-+2+=+c+-+5+
(2) +c+=+a+%2B+3+
----------------------
Plug (2) into (3)
(3) +b%2A%28+a+%2B+3+%29+=+12a+
(3) +b+=+12a+%2F+%28+a+%2B+3+%29+
Plug this into (1)
(1) +a+-+%28+12a+%29%2F%28+a+%2B+3+%29+=+5+
(1) +a%2A%28+a+%2B+3+%29+-12a+=+5%2A%28+a+%2B+3+%29+
(1) +a%5E2+%2B+3a+-+12a+=+5a+%2B+15+
(1) +a%5E2+-+14a+-+15+=+0+
(1) +%28+a+-+15+%29%2A%28+a+%2B+1+%29+=+0+ ( by looking at it )
+a+=+15+ ( can't have a negative age )
and
(2) +c+=+a+%2B+3+
(2) +c+=+18+
and
(1) +a+-+b+=+5+
(1) +15+-+b+=+5+
(1) +b+=+10+
-------------------
+a+-+2+=+13+
+b+-+2+=+8+
+c+-+2+=+16+
-----------------
The girl is 13
Her younger brother is 8
Her older brother is 16
--------------------------
check:
The girl is:
5 yrs older than younger brother YES
3 yrs younger than older brother YES
and
+%28+8+%2B+2+%29%2A%28+16+%2B+2+%29+=+12%2A%28+13+%2B+2+%29+
+10%2A18+=+12%2A15+
+180+=+180+
OK




Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
a girl is currently 5 years older than her younger brother and 3 years younger than her older brother. 2 years from the current time, the product of the ages of the brothers will be 12 times the age of the girl. what is the current age of the oldest OLDER brother
Let the older brother be E

Then girl is: E - 3, and the younger brother is: E - 3 - 5, or E - 8

We then get: (E + 2)(E - 8 + 2) = 12(E - 3 + 2)

(E + 2)(E - 6) = 12(E - 1)

(E + 2)(E - 6) = 12E - 12

E%5E2+-+4E+-+12+=+12E+-+12

E%5E2+-+16E+=+0

E(E - 16) = 0

E - 16 = 0         OR           E = 0 (ignore)

E, or older brother is: highlight_green%28matrix%281%2C2%2C+16%2C+years-old%29%29

That's all....nothing COMPLEX or CONFUSING! It can be done with ONE SIMPLE variable!