To find the number \( x \) such that one third of \( x \) exceeds one fourth of \( x \) by 6, follow these steps:
1. Set up the equation: Let \( x \) be the unknown number. According to the problem, one third of \( x \) exceeds one fourth of \( x \) by 6. This can be written as:
[tex]\[
\frac{1}{3}x - \frac{1}{4}x = 6
\][/tex]
2. Find a common denominator: To simplify the left-hand side of the equation, we need a common denominator for the fractions. The denominators are 3 and 4, and their least common multiple is 12. Rewrite the fractions with the common denominator:
[tex]\[
\frac{4}{12}x - \frac{3}{12}x = 6
\][/tex]
3. Combine the fractions: Now that the fractions have a common denominator, combine them:
[tex]\[
\frac{4x - 3x}{12} = 6
\][/tex]
Simplify the numerator:
[tex]\[
\frac{x}{12} = 6
\][/tex]
4. Solve for \( x \): To isolate \( x \), multiply both sides of the equation by 12:
[tex]\[
x = 6 \times 12
\][/tex]
Perform the multiplication:
[tex]\[
x = 72
\][/tex]
Thus, the number [tex]\( x \)[/tex] is 72.
