Question

40 kyle and erika also played target 100 starting from 52. the expressions they made are shown.
40 kyle
52 + 30 + 10 + 8
40 erika
52 + 20 + 20 + 8
whose expression is equivalent to 52 + 48?
40 kyle 40 erika 40 both 40 neither

Explanation:

Step1: Calculate Kyle's sum

First, we calculate the sum of Kyle's expression: $52 + 30 + 10 + 8$. Let's add the numbers step by step. $30 + 10 = 40$, then $40 + 8 = 48$, and finally $52 + 48 = 100$. But we can also check the sum of the added numbers: $30 + 10 + 8 = 48$, so Kyle's expression is $52 + 48$. Wait, no, wait: $30 + 10 + 8 = 48$? Wait, $30 + 10 = 40$, $40 + 8 = 48$. So Kyle's expression is $52 + 30 + 10 + 8 = 52 + (30 + 10 + 8) = 52 + 48$? Wait, no, $30 + 10 + 8 = 48$? Wait, $30 + 10 = 40$, $40 + 8 = 48$. Yes. Wait, but let's check Erika's: $20 + 20 + 8 = 48$? $20 + 20 = 40$, $40 + 8 = 48$. Oh! Wait, so both Kyle and Erika's expressions: Kyle's added numbers: $30 + 10 + 8 = 48$? Wait, $30 + 10 = 40$, $40 + 8 = 48$. Erika's: $20 + 20 + 8 = 48$? $20 + 20 = 40$, $40 + 8 = 48$. Wait, but the question is which expression is equivalent to $52 + 48$? Wait, no, wait the problem says "equivalent to $52 + 48$"? Wait, no, the problem says "equivalent to $52 + 48$"? Wait, the original problem is "Whose expression is equivalent to $52 + 48$?" Wait, let's recheck.

Wait, Kyle's expression: $52 + 30 + 10 + 8$. Let's sum the numbers after 52: $30 + 10 + 8 = 48$. So $52 + 30 + 10 + 8 = 52 + (30 + 10 + 8) = 52 + 48$. Erika's expression: $52 + 20 + 20 + 8$. Sum the numbers after 52: $20 + 20 + 8 = 48$. So $52 + 20 + 20 + 8 = 52 + (20 + 20 + 8) = 52 + 48$. Wait, but that can't be. Wait, no, wait $30 + 10 + 8 = 48$? $30 + 10 = 40$, $40 + 8 = 48$. Yes. $20 + 20 + 8 = 48$? $20 + 20 = 40$, $40 + 8 = 48$. So both Kyle and Erika's expressions are $52 + 48$? Wait, but let's calculate the total. Kyle: $52 + 30 = 82$, $82 + 10 = 92$, $92 + 8 = 100$. Erika: $52 + 20 = 72$, $72 + 20 = 92$, $92 + 8 = 100$. And $52 + 48 = 100$. So both expressions equal $52 + 48$ (since $48 = 30 + 10 + 8$ and $48 = 20 + 20 + 8$). Wait, but the options are Kyle, Erika, Both, Neither. So the answer should be Both? Wait, no, wait let's check again. Wait, $30 + 10 + 8 = 48$? $30 + 10 = 40$, $40 + 8 = 48$. Yes. $20 + 20 + 8 = 48$? $20 + 20 = 40$, $40 + 8 = 48$. So both Kyle's and Erika's expressions are $52 + 48$ because the sum of their added numbers (after 52) is 48. So both expressions are equivalent to $52 + 48$. Wait, but let's confirm:

Kyle's expression: $52 + 30 + 10 + 8 = 52 + (30 + 10 + 8) = 52 + 48$.

Erika's expression: $52 + 20 + 20 + 8 = 52 + (20 + 20 + 8) = 52 + 48$.

So both are equivalent. Therefore, the correct option is Both.

Step2: Verify Erika's sum

Now, check Erika's expression: $20 + 20 + 8$. $20 + 20 = 40$, $40 + 8 = 48$. So Erika's expression is also $52 + 48$.

Answer:

Both