To determine which mathematical expression correctly represents the phrase "three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]," let's break down the phrase step-by-step.
1. Identifying the "difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]":
- The difference between two numbers [tex]\( t \)[/tex] and [tex]\( y \)[/tex] is obtained by subtracting [tex]\( y \)[/tex] from [tex]\( t \)[/tex].
- Mathematically, this difference is written as [tex]\( t - y \)[/tex].
2. Applying "three times" to the difference:
- To express "three times" of a quantity, we multiply that quantity by 3.
- Here, the quantity is [tex]\( t - y \)[/tex], so three times this difference is written as [tex]\( 3(t - y) \)[/tex].
Now let's match this with the given options:
1. [tex]\( 3(t - y) \)[/tex] matches our derived expression perfectly.
2. [tex]\( 3t - y \)[/tex] represents three times [tex]\( t \)[/tex], then subtract [tex]\( y \)[/tex]. This does not match the phrase "three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]".
3. [tex]\( y - 3t \)[/tex] represents [tex]\( y \)[/tex] minus three times [tex]\( t \)[/tex]. This also does not match the phrase.
Therefore, the correct expression that represents "three times the difference between [tex]\( t \)[/tex] and [tex]\( y \)[/tex]" is:
[tex]\[ 3(t - y) \][/tex]
So, we select the option:
[tex]\[ 1 \][/tex]
Thus, the chosen expression is:
[tex]\[ 3(t - y) \][/tex]
