In a certain two digit number the units digit is one more than three
fourths of the tens digit.
There are only two digits that you can take three-fourths of and get a
whole number. They are 4 and 8. Well, there's 0, but 0 can't be a
first (tens) digit.
So if the tens digit is 4, then three-fourths of 4 is 3.
Then the units digit would be 1 more than 3, so it would be 4.
That would make the number 44.
And if the tens digit is 8, then three-fourths of 8 is 6.
Then the units digit would be 1 more than 6, so it would be 7.
That would make the number 87.
So the number is either 44 or 87.
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If a number which exceeds the given number by 100 is divided by the sum of the
digits of the given number, the quotient is twelve with the remainder of five.
If the number is 44, then the number which exceeds it by 100 is 144.
The sum of the digits would be 4+4=8.
So let's divide 144 by 8:
18
8)144
8
64
64
0
No, that quotient is not twelve with the remainder of five. It's 18
with a remainder of 0, so the number is not 44, so it must be 87.
But let's check that out. Sometimes people post bogus problems with
no solution.
If the number is 87, then the number which exceeds it by 100 is 187.
The sum of the digits would be 8+7=15.
So let's divide 187 by 15:
12
15)187
15
37
30
7
Well the quotient is indeed 12, but the remainder is 7, not 5, so this is
a bogus problem. There is no solution.
Edwin