To write the given statements ("Sara spent [tex]$2 more than Lauren," and "together they spent $[/tex]19") as an equation, follow these steps:
1. Let's denote the amount of money that Lauren spent as [tex]\( l \)[/tex].
2. Since Sara spent [tex]$2 more than Lauren, we can denote the amount of money Sara spent as \( s \). Therefore, \( s = l + 2 \).
The first statement translates into the equation:
\[ s = l + 2 \]
3. Next, we know that together they spent $[/tex]19. This can be written as:
[tex]\[ s + l = 19 \][/tex]
4. Combining these two pieces of information, we have the system of equations:
[tex]\[ s = l + 2 \][/tex]
[tex]\[ s + l = 19 \][/tex]
We now look at the options provided and choose the correct equation that matches our system.
- A. [tex]\( 19 - k + (k + 1) \)[/tex]
This option does not fit our system.
- B. [tex]\( s + 2 = 19 \)[/tex]
This option is incorrect because it does not represent that Sara spent [tex]$2 more than Lauren.
- C. \( m = m + 2 \)
This is incorrect as it is a trivial equation and does not relate to the problem at hand.
- D. \( l + (l + 2) = 19 \)
This option correctly represents the scenario. The left-hand side (\( l + (l + 2) \)) translates to the total amount spent by Lauren and Sara, and the right-hand side (19) is the total amount spent.
Option D accurately represents both given statements, which are:
1. Sara spent $[/tex]2 more than Lauren, [tex]\( s = l + 2 \)[/tex].
2. Together they spent $19, [tex]\( l + (l + 2) = 19 \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{l + (l + 2) = 19} \][/tex]
