College Algebra Word Problem

Question

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 twelve times the age of the girl. What is the current age of the older brother? 

Answer 1

Let x = girl's age now

 

Then, x - 5 = younger brother's age now

         x + 3 = older brother's age now

 

Ages in two years:  girl   x+2

                            younger brother    (x-5) + 2 = x-3

                            older brother        (x+3) + 2 = x+5

 

(x-3)(x+5) = 12(x+2)

 

So, x² + 2x - 15 = 12x + 24

 

     x² - 10x - 39 = 0

 

     (x-13)(x+3) = 0

 

                  x = 13 or x = -3

 

Since x can't be negative, x = 13

 

Older brother's age now = x+3 = 16

 

 

Answer 2

y represents younger brother

g represents girl

o represents older brother

 

At the present:

 

y represents the age of the younger brother

y + 5 represents the age of the girl

y + 5 + 3 represents the age of the older brother

 

In two years

 

y + 2 represents the age of the younger brother

y + 7 represents the age of the girl

y + 10 represents the age of the older borther

 

(y + 2)(y + 10) = 12(y + 7)            multiply

y² + 12y + 20 = 12y + 84              subtract 12y from both sides

y² + 20 = 84                                  subtract 20 from both sides

y² = 64

y = ±8

 

The younger brother is 8. You calculate the age of the older brother.