- Identify the variable \(y\) as the unknown number.
- Translate "the product of a number and 5" as \(5y\).
- Add "eight more" to get \(5y + 8\).
- Set the expression equal to 9 to form the final equation: \(\boxed{5y + 8 = 9}\).
Explanation
- Translating the Sentence into an Equation
To translate the given sentence into a mathematical equation, we break down the phrase into its logical components. We are given the variable \(y\) to represent the unknown number.
- "a number" is represented by \(y\).
- "the product of a number and 5" means we multiply the variable \(y\) by 5, resulting in \(5y\).
- "Eight more than" indicates addition, so we add 8 to our previous expression: \(5y + 8\).
- "is 9" represents equality to the value 9.
By combining these parts, we form the equation \(5y + 8 = 9\).
Examples
Translating verbal descriptions into algebraic equations is a foundational skill in mathematics, useful for solving real-world problems. For example, if you know a subscription service costs a base fee of \$\$8\$ per month plus a rate of \$\$5\$ per additional service unit, and your total monthly bill is \$\$9\$, you can represent this situation with the equation \(5y + 8 = 9\), where \(y\) is the number of extra service units used. This allows you to solve for \(y\) to determine exactly how many units you utilized.