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the standard addition algorithm below is being used to add three two-digit numbers 4z + 27 + x 5 equals y 14. If x, y, and z each represent a different digit from 0 to 9 what is the value of (x)(y)(z)?

the standard addition algorithm below is being used to add three two-digit numbers-example-1
User Linear
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For the units positions of all numbers we have:

z+7+5=4 \\ z+12=4
From this we can conclude that total sum of these three numbers is 14. Number 1 we carry to next step. So we have:

z+12=14 \\ z=2

For the tens positions of all numbers we have:

4+2+x+1=1 \\ 7+x=1
The extra number 1 on left side comes from the carry from last step. Similar to ones position we know that total sum is 11.

7+x=11 \\ x=4

Now we insert x and z to find out y:

42+27+45=y14 \\ 114=y14 \\ y=1

Now we need to find out the product of these three numbers:

x*y*z=4*1*2=8
User Zory
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