Answer :
To solve the problem where Marley checked her subtraction, we need to determine which pair of number sentences confirms that her solution is correct.
First, let's look at Marley's subtraction:
[tex]\[ 345 - 176 = 169 \][/tex]
Now we need to check which pair of number sentences correctly verifies this solution. We'll do this by examining each pair of sentences given in the options:
### Option A:
1. [tex]\( 345 - 176 = 169 \)[/tex]
2. [tex]\( 176 - 169 = 7 \)[/tex]
Checking the first statement: [tex]\( 345 - 176 = 169 \)[/tex]. This is correct based on Marley's solution.
Checking the second statement: [tex]\( 176 - 169 = 7 \)[/tex]. This is not correct because:
[tex]\[ 176 - 169 = 7 \quad \text{(which is true)} \][/tex]
This pair, therefore, has inconsistent logic for verification.
### Option B:
1. [tex]\( 345 - 176 = 169 \)[/tex]
2. [tex]\( 345 + 176 = 521 \)[/tex]
Checking the first statement: [tex]\( 345 - 176 = 169 \)[/tex]. This is correct.
Checking the second statement: [tex]\( 345 + 176 = 521 \)[/tex]. This does not relate logically to verifying the initial subtraction.
### Option C:
1. [tex]\( 345 - 176 = 169 \)[/tex]
2. [tex]\( 345 - 169 = 176 \)[/tex]
Checking the first statement: [tex]\( 345 - 176 = 169 \)[/tex]. This is correct.
Checking the second statement: [tex]\( 345 - 169 = 176 \)[/tex]. Here we verify the original subtraction because if:
[tex]\[ 345 - 169 = 176 \quad \text{(which is true)} \][/tex]
This shows that changing the order of subtraction still holds true.
### Option D:
1. [tex]\( 345 - 176 = 169 \)[/tex]
This option does not provide a complementary step to verify the correctness.
Given the analysis, the only option that provides correct and logical verification for Marley's solution is:
[tex]\[ \boxed{C} \][/tex]
First, let's look at Marley's subtraction:
[tex]\[ 345 - 176 = 169 \][/tex]
Now we need to check which pair of number sentences correctly verifies this solution. We'll do this by examining each pair of sentences given in the options:
### Option A:
1. [tex]\( 345 - 176 = 169 \)[/tex]
2. [tex]\( 176 - 169 = 7 \)[/tex]
Checking the first statement: [tex]\( 345 - 176 = 169 \)[/tex]. This is correct based on Marley's solution.
Checking the second statement: [tex]\( 176 - 169 = 7 \)[/tex]. This is not correct because:
[tex]\[ 176 - 169 = 7 \quad \text{(which is true)} \][/tex]
This pair, therefore, has inconsistent logic for verification.
### Option B:
1. [tex]\( 345 - 176 = 169 \)[/tex]
2. [tex]\( 345 + 176 = 521 \)[/tex]
Checking the first statement: [tex]\( 345 - 176 = 169 \)[/tex]. This is correct.
Checking the second statement: [tex]\( 345 + 176 = 521 \)[/tex]. This does not relate logically to verifying the initial subtraction.
### Option C:
1. [tex]\( 345 - 176 = 169 \)[/tex]
2. [tex]\( 345 - 169 = 176 \)[/tex]
Checking the first statement: [tex]\( 345 - 176 = 169 \)[/tex]. This is correct.
Checking the second statement: [tex]\( 345 - 169 = 176 \)[/tex]. Here we verify the original subtraction because if:
[tex]\[ 345 - 169 = 176 \quad \text{(which is true)} \][/tex]
This shows that changing the order of subtraction still holds true.
### Option D:
1. [tex]\( 345 - 176 = 169 \)[/tex]
This option does not provide a complementary step to verify the correctness.
Given the analysis, the only option that provides correct and logical verification for Marley's solution is:
[tex]\[ \boxed{C} \][/tex]
