Chapter 1.5, Problem 3WE

To determine

To check: whether one of the two given equation is a translation of the given statement.

Answer to Problem 3WE

The equation which gives the correct translation of the statement is $\text{a}\text{.}$

Explanation of Solution

Given Information: The statement “Half of the sum of the three and a number is four” and two possible expressions which is to be checked for translation.

The given statement represents a mathematic expression separated by an equality sign which can be decoded as follows.

Considering left-hand side of the expression,

(1)One part of the left hand side of the expression consists of the sum of two numbers one being unknown and other being 3. This can be represented symbolically as $3+n$ .

(2) The second part of the statement says half of the sum of three and a number. This implies half of the sum in (1). This can be expressed as $\frac{1}{2}\left(3+n\right)$

The right-hand side of the expression consists of the number 4.

Thus, the final expression is given by,

  $\frac{1}{2}\left(3+n\right)=4$

Based on the given options the option a. gives the expression $\frac{1}{2}\left(3+n\right)=4$ and the option b. gives $\frac{1}{2}.3+n=4$ . Comparing, the result obtained, it can be seen that option a. represents the correct translation of the given statement.