The sum of two numbers one of which is 3/4 of the other is 84 . Find the number
the two numbers are in the ratio 4:3
divide 84 into 7 parts.
see where that gets you.
a / b = 3 / 4 Multiply both sides by b
a = ( 3 / 4 ) b
a + b = 84
( 3 / 4 ) b + b = 84
( 3 / 4 ) b + ( 4 / 4 ) b = 84
( 7 / 4 ) b = 84 Multiply both sides by 4
7 b = 84 * 4
7 b = 336 Divide both sides by 7
b = 336 / 7 = 48
b = 48
a = ( 3 / 4 ) b = 3 * 48 / 4 = 144 / 4 = 36
a = 36
a / b = 36 / 48 = 3 * 12 / ( 4 * 12 ) = 3 / 4
To find the numbers, let's assume one of the numbers as 'x'.
Given that one of the numbers is 3/4 of the other, we can express the second number as (3/4)x.
According to the given condition, the sum of the two numbers is 84. So, we can write the equation as:
x + (3/4)x = 84
To solve this equation, we need to first combine the like terms:
(4/4)x + (3/4)x = 84
Now, we can simplify the equation:
(7/4)x = 84
To solve for x, we can multiply both sides of the equation by the reciprocal of (7/4), which is (4/7):
(7/4)x * (4/7) = 84 * (4/7)
This simplifies to:
x = 336/7
x = 48
So, one of the numbers is 48.
To find the other number, you can substitute the value of x back into the equation:
(3/4)x = (3/4)*48 = 36
The other number is 36.
Therefore, the two numbers are 48 and 36.