Questions: Using the variable x, translate the sentence into an equation. Solve the resulting equation. If a number is increased by 14 and then divided by 5, the result is 5.

Solution Steps

To translate the given sentence into an equation, we need to follow these steps:

1. Identify the unknown number and represent it with the variable \( x \).
2. Translate the phrase "increased by 14" to \( x + 14 \).
3. Translate the phrase "then divided by 5" to \( \frac{x + 14}{5} \).
4. Set the resulting expression equal to 5, as stated in the problem.

The resulting equation is: \[ \frac{x + 14}{5} = 5 \]

To solve the equation:

1. Multiply both sides by 5 to eliminate the fraction.
2. Subtract 14 from both sides to isolate \( x \).

The problem states: "If a number is increased by 14 and then divided by 5, the result is 5."

We represent the unknown number as \( x \). The phrase "increased by 14" translates to \( x + 14 \). The phrase "then divided by 5" translates to \( \frac{x + 14}{5} \). Setting this equal to 5, we get the equation: \[ \frac{x + 14}{5} = 5 \]

To solve the equation \( \frac{x + 14}{5} = 5 \):

1. Multiply both sides by 5 to eliminate the fraction: \[ x + 14 = 25 \]
2. Subtract 14 from both sides to isolate \( x \): \[ x = 25 - 14 \] \[ x = 11 \]

Final Answer