Question #91125

1 Answer
Bisma J.
Dec 22, 2017

Convert the sentences into algebraic equations between each digit, then solve to get #0.013#.

Explanation:

Since the digits mentioned are the tenth place, the hundreth place, and a "last" digit, we could assume that this decimal must have three digits, as in

#"0.ABC"#,

where #A# is the tenth place, #B# is the hundredth place and #C# is the thousandth place, or the last digit.

The information given is that the last digit is three, so

#C = 3#,

Then the tenth place, #A#, is compared to the two other digits:

"you will find (that the tenth place is) a digit one less than the digit in my hundreth place ..."

which means

#A = B - 1#,

"... and (the tenth place is) three less than my other digit (which is the last digit)."

which means

#A = C - 3#.

Since we know #C = 3#, we immediately get that

#A = C - 3 = 3 - 3 = 0#,

and since we now know the value of #A#, we could solve for #B#:

#A = B - 1 rarr 0 = B - 1#

Simply add #1# to both sides of the equation to get #B = 1#.

So we have #A = 0#, #B = 1# and #C = 3#, meaning that the decimal must be #0.013#.

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