Number Word Problem Solution
Let the unknown number be represented by the variable '$x$'. The problem states that one-sixth of the number exceeds its one-ninth by 100.
Setting up the Algebraic Equation
We can translate the problem into an algebraic equation:
- One-sixth of the number: $\frac{x}{6}$
- One-ninth of the number: $\frac{x}{9}$
- The condition "one-sixth of a number exceeds its one-ninth by 100" translates to:
$ \frac{x}{6} = \frac{x}{9} + 100 $
Solving for the Number
To find the value of '$x$', we need to solve the equation:
- Subtract $\frac{x}{9}$ from both sides to isolate the term with '$x$': $ \frac{x}{6} - \frac{x}{9} = 100 $
- Find a common denominator for 6 and 9, which is 18. Rewrite the fractions with the common denominator: $ \frac{3x}{18} - \frac{2x}{18} = 100 $
- Combine the fractions on the left side: $ \frac{3x - 2x}{18} = 100 $ $ \frac{x}{18} = 100 $
- Multiply both sides by 18 to solve for '$x$': $ x = 100 \times 18 $ $ x = 1800 $
Therefore, the number is 1800.
Verification
Check if the solution is correct:
- One-sixth of 1800: $\frac{1800}{6} = 300$
- One-ninth of 1800: $\frac{1800}{9} = 200$
- Difference: $300 - 200 = 100$. The condition is satisfied.
The number is 1800.
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
