The number that satisfies the given condition is -72.
Let's break down the given statement step by step:
The difference of a number and 24:
Let's assume the number is represented by 'x'.
The difference of 'x' and 24 can be written as (x - 24).
Divided by 8: We divide the difference of 'x' and 24 by 8, which gives us ((x - 24) / 8).
The quotient of the difference of a number and 24 divided by 8: So, the quotient is ((x - 24) / 8).
The number divided by 6: We divide the number 'x' by 6, which gives us (x / 6).
The given statement says that the quotient obtained in step 3 is equal to the number divided by 6.
Mathematically, we can represent this as:
((x - 24) / 8) = (x / 6)
To solve this equation for 'x', we can cross-multiply:
6(x - 24) = 8x
Now, we can simplify and solve for 'x':
6x - 144 = 8x
Subtracting 6x from both sides:
-144 = 2x
Dividing by 2:
x = -72
Therefore, the number that satisfies the given condition is -72.
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