7. 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)?

To solve this problem, we need to follow the standard addition algorithm and find the values of x, y, and z.

Let's start by adding the digits in the ones place column:
z + 7 + 5 = 14

Since the sum of these three digits is 14, we can conclude that z must be equal to 2 (since 4z can't be greater than 8).

Next, we move to the tens place column:
2 + 2 + x = 13

To get a sum of 13, we need x to be 9 (since the highest digit available is 9).

Lastly, we move to the hundreds place column:
1 + 0 + y = 1

To get a sum of 1, y must be equal to 1.

Therefore, the digits x, y, and z are 9, 1, and 2 respectively. So, the value of (x)(y)(z) is 9 * 1 * 2 = 18.

To find the value of (x)(y)(z), we need to solve the addition problem by working with each column of digits individually.

Let's start with the rightmost column (the units place). The equation is:

z + 7 + 5 = 14

Since z represents a digit from 0 to 9, we cannot have a two-digit sum. Therefore, z must be 2, because 2 + 7 + 5 = 14.

Next, we move to the tens place. The equation is:

4 + 2 + x = 3

Here, we can see that x must be 7 because 4 + 2 + 7 = 13, and 13 is greater than 3.

Finally, we move to the hundreds place. The equation is:

1 + x + y = 0

Since x is 7, we substitute it into the equation:

1 + 7 + y = 0

Simplifying further, we have:

8 + y = 0

To solve for y, we subtract 8 from both sides:

y = -8

However, y represents a digit from 0 to 9, so a negative number is not possible. Therefore, there is no valid solution for y in this case.

In summary, the value of (x)(y)(z) cannot be determined because there is no valid solution for y.

Come on - this one is easy.

You have z+7+5 ends in 4
7+5=12, so z=2

Now work with that same idea to get x.

Remember that no one said that x,y,z had to be different from all the other digits already present.