explain how to solve this: Below, the standard addition algorithm is being used to add three two-digit numbers.

4z

27

+x5

y14

If x, y and z each represent a different digit from 0 to 9, what is the value of (x)(y)(z)?

Let's break down how to solve the problem step by step. We are given three two-digit numbers being added together in a standard addition algorithm, and we need to find the values of \( x \), \( y \), and \( z \). Here's the setup:

\[
\begin{array}{c@{}c@{}c@{}c@{}c}
 & 4 & z \\
+ & 2 & 7 \\
+ & x & 5 \\
\hline
 & y & 1 & 4 \\
\end{array}
\]

### Step 1: Analyze the ones place

- The digits in the ones place are \( z \), \( 7 \), and \( 5 \).
- Adding these gives \( z + 7 + 5 \).
- From the result, the ones digit is 4. This means \( z + 7 + 5 \) must end in 4.

Thus:
\[
z + 7 + 5 = 10k + 4 \quad \text{(where \( k \) is an integer)}
\]
Simplifying:
\[
z + 12 = 10k + 4
\]
\[
z = 10k + 4 - 12
\]
\[
z = 10k - 8


Learn how to solve the addition of three two-digit numbers using the standard addition algorithm. Find the values of x, y, and z to complete the equation. Suitable for elementary school students in Grades 3-4.

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