To determine which expression is equivalent to [tex]\( 100 + 20 \)[/tex], let's evaluate each option step-by-step.
First, we start by calculating the given expression:
[tex]\[ 100 + 20 = 120 \][/tex]
Next, let's evaluate each of the provided options and compare their results to 120:
1. Option 1: [tex]\( 5(20 + 4) \)[/tex]
[tex]\[
5(20 + 4) = 5 \cdot 24 = 120
\][/tex]
This option evaluates to 120.
2. Option 2: [tex]\( 10(10 + 10) \)[/tex]
[tex]\[
10(10 + 10) = 10 \cdot 20 = 200
\][/tex]
This option evaluates to 200.
3. Option 3: [tex]\( 10(10 + 3) \)[/tex]
[tex]\[
10(10 + 3) = 10 \cdot 13 = 130
\][/tex]
This option evaluates to 130.
4. Option 4: [tex]\( 5(20 + 3) \)[/tex]
[tex]\[
5(20 + 3) = 5 \cdot 23 = 115
\][/tex]
This option evaluates to 115.
After comparing the results:
- Option 1 evaluates to 120, which is equivalent to the original expression [tex]\(100 + 20\)[/tex].
- Options 2, 3, and 4 do not evaluate to 120 and thus are not equivalent to the original expression.
Therefore, the expression that is equivalent to [tex]\( 100 + 20 \)[/tex] is:
[tex]\[ \boxed{5(20 + 4)} \][/tex]
