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)?
Put your data horizontally, so it can be understood.
To find the value of (x)(y)(z), we need to add the given three two-digit numbers using the standard addition algorithm:
```
4z
+ 27
+ x5
+ y14
------
```
Let's start by adding the rightmost column (the ones place):
```
4z
27
+ x5
+ y14
------
??
```
The sum of the ones column is given by z + 7 + 5 + 4 = z + 16. So, we write down the units digit of this sum and carry the tens digit over to the tens column:
```
4z
27
+ x5
+ y14
------
?6
```
Now, let's add the tens column:
```
4z
27
+ x5
+ y14
------
??
+??
```
The sum of the tens column is given by 1 (carried over) + z + 2 + x + y. So, we write down the units digit of this sum:
```
4z
27
+ x5
+ y14
------
??
+????
= 9
```
From the equation above, we can deduce that the sum of the tens column is equal to 9:
1 + z + 2 + x + y = 9
We can try different values for z, x, and y to solve the equation. But since it's mentioned that x, y, and z each represent different digits from 0 to 9, we can use trial and error:
Let's start with z = 2:
1 + 2 + 2 + x + y = 9
Simplifying, we get:
5 + x + y = 9
x + y = 4
To make x + y = 4, one possibility is x = 3 and y = 1.
Therefore, (x)(y)(z) = 3 * 1 * 2 = 6.
So, the value of (x)(y)(z) is 6.