Question

Anna found the difference between thirteen and the product of four and a number. Which expression represents this phrase, and what is its value if n = 3?
StartFraction n Over 4 EndFraction minus 13; when n = 3 the value is Negative 12 and one-fourth
13 minus 4 n; when n = 3 the value is 1
4 n minus 13; when n = 3 the value is –1
13 minus StartFraction n Over 4 EndFraction; when n = 3 the value is 12 and one-fourth

Answer 1

Let's break down the phrase: "the difference between thirteen and the product of four and a number".

1. "the product of four and a number" can be expressed as \( 4n \).
2. "the difference between thirteen and" that product can be expressed as \( 13 - 4n \).

Now we have the expression \( 13 - 4n \).

Next, let's evaluate this expression when \( n = 3 \):
\[
13 - 4(3) = 13 - 12 = 1
\]

Therefore, the correct expression is:
**\( 13 - 4n \)**, and when \( n = 3 \), the value is **1**.

Now, let's summarize the expressions given and their values when \( n = 3 \):

1. \( \frac{n}{4} - 13 \); when \( n = 3 \) the value is \( \frac{3}{4} - 13 = -12.25 \) (which is incorrect)
2. \( 13 - 4n \); when \( n = 3 \) the value is \( 1 \) (this is the correct one)
3. \( 4n - 13 \); when \( n = 3 \) the value is \( 12 - 13 = -1 \) (incorrect)
4. \( 13 - \frac{n}{4} \); when \( n = 3 \) the value is \( 13 - \frac{3}{4} = 12.25 \) (incorrect)

Thus, the only correct statement is:
**The expression that represents the phrase is \( 13 - 4n \) and its value when \( n = 3 \) is \( 1 \).**