1.5 #5 - Please help me solve this!!

Algebra
Tutor: None Selected Time limit: 1 Day

A girl is currently 5 years older than her younger brother and 3 years younger than her older brother. Two 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 older brother?

Oct 3rd, 2015

Thank you for the opportunity to help you with your question! IF you have any clarification, please don't hesitate to ask and I will do my best to answer. ++++++++++++

Let YB = younger brother’s age

Let OB = older brother’s age

Let YB + 5 = OB – 3 = girl’s age

Equation 1

YB + 2 + (OB + 2)  = 12*(YB + 5 + 2)

YB+2+OB+2 = 12(YB+7)

12YB+84 = YB+OB+4

12YB-YB-4+84=OB

OB=11YB+80

Equation 2

YB + 5 = OB – 3

Substitute OB

YB+5=(11YB+80)-3

YB+5=11YB+77

11YB=YB+5

11YB-YB=5

10YB=5

YB = 5/10 or 0.5 year or 6 months


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 18th, 2015

Final ANSWER: (please ignore the first one. It was the wrong file)

Let YB = younger brother’s age

Let OB = older brother’s age

Let G = girl’s age

Let YB + 5 = OB – 3 = girl’s age

ð  OB=YB+8

 (YB+2)*(OB+2)=12*(G+2)

YBOB+2OB+2YB+4=12G+24

YBOB+2OB+2YB+4=12*(YB+5)+24

YBOB+2OB+2YB+4 = 12YB+60+24

YBOB+2OB=10YB+80

YBOB+2(YB+8)=10YB+80

YBOB=8YB+64

OB = 8+64/YB

Substitute

YB + 5 = OB – 3

YB+5=(8+64/YB) – 3

YB+5=5 +64/YB

YB=64/YB

YB^2=64

Yb=SQUAREROOT OF 64

YB = younger brother’s age = 8

Girl’s age = 13

Older brother’s age = 16


Sep 18th, 2015

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