FIND THE FRACTION

Question

Q: The sum of two fractions is 3 times their differences. Six times the smaller fraction exceeds the larger fraction by 3/2 . Find the fractions.

Answer 1

Let x = the larger fraction and y = the smaller one.  We have two unknowns (x and y) so we need two equations to find their values,

 

Equation 1 - The sum of two fractions (x+y) is three times their difference (3(x-y)): x+y = 3(x-y)

 

Equation 2 - Six times the smaller fraction (6y) exceeds the larger fraction by 3/2 (x+3/2):  6y = x + (3/2)

 

Find x:

x + y = 3x - 3y

4y = 2x

y = x/2

 

Substitute x/2 for y in equation 2:

 

6y = x + 3/2

6(x/2) = x + 3/2

3x = x + 3/2

2x = 3/2

 

x = 3/4

 

Find y:

 

 y = x/2 = (3/4)*(1/2) = 3/8

 

Check:

x+y = 3(x-y)

3/4 + 3/8 = 3(3/4-3/8)

9/8 = 3(3/8)

9/8 = 9/8    CHECK!

 

6y = x + 3/2

6(3/8) = 3/4 + 3/2

18/8 = 9/4

9/4 = 9/4     CHECK!