Question

tiana and yusuf each write an expression to help make $28 + 54$ easier to add.
tiana
$28 + 2 + 54$
yusuf
$28 + 2 + 52$
whose expression has the same value as $28 + 54$?
tiana yusuf both neither

Explanation:

Step1: Calculate Tiana's expression

Tiana's expression is \(28 + 2 + 54\). First, add \(28\) and \(2\): \(28+2 = 30\). Then add \(30\) and \(54\): \(30 + 54 = 84\). Now, calculate the original expression \(28 + 54 = 82\)? Wait, no, wait: \(28+54 = 82\)? Wait, no, \(28 + 54\): \(28+50 = 78\), \(78 + 4 = 82\)? Wait, no, \(28+54\): \(20+50 = 70\), \(8 + 4 = 12\), \(70+12 = 82\). Wait, Tiana's expression: \(28+2 = 30\), \(30+54 = 84\). Wait, that can't be. Wait, maybe I made a mistake. Wait, no, the original problem is to check if the expressions are equal to \(28 + 54\). Let's recalculate.

Wait, Tiana's expression: \(28 + 2 + 54\). Let's use associative property: \((28 + 2)+54 = 30 + 54 = 84\). Original expression: \(28 + 54 = 82\)? Wait, no, \(28 + 54\) is \(82\)? Wait, \(28 + 50 = 78\), \(78 + 4 = 82\). Tiana's: \(30 + 54 = 84\). Now Yusuf's expression: \(28 + 2 + 52\). Let's calculate: \(28 + 2 = 30\), \(30 + 52 = 82\). Ah, I see, I messed up Tiana's. Wait, no, Tiana's is \(28 + 2 + 54\), Yusuf's is \(28 + 2 + 52\). Original is \(28 + 54\). Let's check Yusuf's: \(28 + 2 + 52 = 28 + (2 + 52) = 28 + 54\), which is the original expression. Tiana's: \(28 + 2 + 54 = (28 + 2) + 54 = 30 + 54 = 84\), while original is \(28 + 54 = 82\)? Wait, no, \(28 + 54\) is \(82\)? Wait, \(28 + 54\): \(28 + 50 = 78\), \(78 + 4 = 82\). Tiana's: \(30 + 54 = 84\). Yusuf's: \(28 + 2 + 52 = 30 + 52 = 82\), which is equal to \(28 + 54\). So Yusuf's expression is equal. Wait, but let's do it again.

Yusuf's expression: \(28 + 2 + 52\). Let's combine \(2 + 52 = 54\), so \(28 + (2 + 52) = 28 + 54\), which is the original expression. So Yusuf's expression is equal. Tiana's: \(28 + 2 + 54 = (28 + 2) + 54 = 30 + 54 = 84\), while original is \(28 + 54 = 82\). Wait, that's a problem. Wait, no, maybe I miscalculated \(28 + 54\). Let's do \(28 + 54\): \(28 + 50 = 78\), \(78 + 4 = 82\). Tiana's: \(30 + 54 = 84\). Yusuf's: \(30 + 52 = 82\), which is equal to \(28 + 54\). So Yusuf's expression is equal. So the answer is Yusuf.

Wait, but let's check again. Yusuf's expression: \(28 + 2 + 52\). Let's add \(2 + 52 = 54\), so \(28 + 54\), which is the original. So Yusuf's expression is equal. Tiana's: \(28 + 2 + 54 = 30 + 54 = 84\), which is not equal to \(28 + 54 = 82\). So only Yusuf's expression has the same value.

Step2: Confirm with properties

Using the associative property of addition, \(a + b + c = a + (b + c)\). For Yusuf: \(28 + 2 + 52 = 28 + (2 + 52) = 28 + 54\), which matches the original. For Tiana: \(28 + 2 + 54 = (28 + 2) + 54 = 30 + 54\), which is not equal to \(28 + 54\).

Answer:

Yusuf (the option: Yusuf)