the difference between three fourths and three fifths of a number is 9 determine the number
(3/4 - 3/5)x = 9
3/20 x = 9
x = 60
check:
3/4 * 60 = 45
3/5 * 60 =36
45-36 = 9
To determine the number, we can use algebraic equations. Let's assign the unknown number as "x".
The difference between three-fourths and three-fifths of a number is 9, so we can write an equation:
(3/4)x - (3/5)x = 9
To solve this equation, we need to find a common denominator for the fractions, which is 20. Let's convert the fractions:
(15/20)x - (12/20)x = 9
Now, we can combine like terms:
(3/20)x = 9
To isolate "x", we can multiply both sides of the equation by the reciprocal of the fraction (20/3):
x = 9 * (20/3)
Simplifying further:
x = 60
Therefore, the number is 60.