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morpeh [17]
3 years ago
13

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 eac

h represent a different digit from 0 to 9 what is the value of (x)(y)(z)?

Mathematics
1 answer:
Studentka2010 [4]3 years ago
3 0
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
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