Question

How do you write an equation for the verbal statement, “three times the sum of a number n and 7 is 16”?

Answer 1

Hint: To express a verbal phrase as an algebraic expression, we need to break the phrase into different parts. Write the mathematical expression for each part, and finally combine the expressions for all the parts, we get the algebraic expression for the given phrase.

Complete step by step answer:
The given phrase is the three times the sum of a number n and 7 is 16. We will break this phrase into three parts.
The first part is ‘three times’. This means that we have to take a product of two quantities, first of them is 3. The other quantity can be found using the next part.
The second part of the phrase is ‘sum of a number n and 7’. Thus, the other quantity in the multiplication is summation of variable n and 7. We can express this algebraically as \[(n+7)\].
The last part of this phrase is ‘ is 16’. This part means we have to equate the expression before it to 16.
Now that we have converted all parts into mathematical expressions, we need to combine them to form the expression for the given phrase. By doing this we get \[3(n+7)=16\]
Hence, the expression for the given phrase is \[3(n+7)=16\].

Note: The expression we have written is a linear equation in one variable. We can easily solve this equation to find the solution value of the variable. We can do a similar thing to convert an algebraic expression to a verbal phrase. We need to break the equation into different parts and write verbal meaning for each part. After this after combining the verbal meaning of each phrase, we get the verbal expression.