Question #1a0d7

2 Answers
Mar 20, 2017

Answer:

#"the number is "36#

Explanation:

If we let the number be represented by n

Change the fractions to eqivalent fractions with a #color(blue)"common denominator"#

#rArr1/3=1/3xx4/4=4/12" and " 1/4=1/4xx3/3=3/12#

#rArr4/12x-3/12x=3larrcolor(red)" difference"#

Since the fractions have a common denominator we can subtract the numerators while leaving the denominator as it is.

#rArr(4x)/12-(3x)/12=x/12#

#rArrx/12=3#

multiply both sides by 12

#cancel(12)^1xxx/cancel(12)^1=12xx3#

#rArrx=36#

#color(blue)"As a check"#

#1/3xx36-1/4xx36=12-9=3to" True"#

#rArr" The number is "36#

Mar 20, 2017

Answer:

36

Explanation:

Let the number be x
One third of the number is #x / 3 # and one fourth of the number is #x / 4#. The difference between the two is #x / 3 - x / 4#, which is equal to 3
ie #x / 3 - x / 4 = 3#
The Lowest common Multiple, (LCM) of the denominators namely , is 12
Multiplying through out by 12, we get,

#x / 3 * 12 - x / 4 * 12 = 3 * 12#
or
#4x - 3x = 36#
ie # x = 36#