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Question 892975: Mico's house number has three digits. Removing the leftmost digit gives Ben's house number. Removing the leftmost digit of Ben's house number gives Ciara's house number. The sum of the three house numbers is 912. What is the middle digit of Mico's house number?
Answer by Edwin McCravy(20060) (Show Source):
You can put this solution on YOUR website! Mico's house number has three digits. Removing the leftmost digit gives Ben's
house number. Removing the leftmost digit of Ben's house number gives Ciara's
house number. The sum of the three house numbers is 912. What is the middle
digit of Mico's house number?
Let h = the hundreds digit (of Mico's house number)
Let t = the tens digit
Let u = the units digit
So the house numbers written in digit form are
Mico's house number = htu.
Ben's house number = tu.
Clara's house number = u.
We form the arithmetic (basic math) addition:
htu
tu
u
---
912
In the right column To get the 2 at the bottom, the 3 u's have
to be 4 so they'll add up to 12 and there'll be 1 to carry. So
we have this:
1
ht4
t4
4
---
912
Looking at the middle column of digits, either the two t's are 0
so the middle column of digits will add up to 1, or the two t's
are 5 so that the middle column will add up to 11 with 1 to carry.
But t can't be 0 because that would make Ben's house number 04.
But nobody writes 04, they just write 4. So if you removed the
leftmost digit of 4 you would have nothing at all! So 0 is out.
Therefore t = 5 (That's the answer).
Completing the addition:
11
h54
54
4
---
912
Since we have 1 to carry to the left column,
which gives us a 9 at the bottom left, h can
only be 8.
11
854
54
4
---
912
The house numbers are 854, 54, and 4 and the
middle digit of Mico's house number is 5.
Edwin
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