nine more than the quotient of a number and 8 is equal to 3 Use the variable w for the unknown number.
The Correct Answer and Explanation is:
Equation:
Nine more than the quotient of a number and 8 is equal to 3.
Step 1: Translate the words into an algebraic equation.
Let the unknown number be represented by the variable www.
“The quotient of a number and 8” means w8\frac{w}{8}8w.
“Nine more than” this quotient means w8+9\frac{w}{8} + 98w+9.
This expression is “equal to 3,” so the full equation is:w8+9=3\frac{w}{8} + 9 = 38w+9=3
Step 2: Solve the equation.
Start by isolating the variable term.
Subtract 9 from both sides:w8+9−9=3−9\frac{w}{8} + 9 – 9 = 3 – 98w+9−9=3−9w8=−6\frac{w}{8} = -68w=−6
Next, multiply both sides by 8 to eliminate the denominator:8⋅w8=−6⋅88 \cdot \frac{w}{8} = -6 \cdot 88⋅8w=−6⋅8w=−48w = -48w=−48
Final Answer:w=−48w = -48w=−48
Explanation (Textbook Style):
In solving algebraic equations that involve words, the first step is to translate the written statement into a mathematical equation. The phrase “the quotient of a number and 8” refers to a division, specifically dividing a number www by 8, which gives the expression w8\frac{w}{8}8w. Next, the phrase “nine more than” tells to add 9 to this expression, resulting in w8+9\frac{w}{8} + 98w+9. This sum is stated to be equal to 3, which sets up the equation w8+9=3\frac{w}{8} + 9 = 38w+9=3.
To solve this equation, begin by simplifying it. Subtracting 9 from both sides isolates the fraction:w8=−6\frac{w}{8} = -68w=−6
Then, to eliminate the denominator and solve for the variable www, multiply both sides of the equation by 8:w=−48w = -48w=−48
Thus, the value of the unknown number is −48-48−48. This means that if −48-48−48 is divided by 8, the result is −6-6−6, and adding 9 to this gives the final value of 3, which confirms the correctness of the solution.
