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u-can-do
Fractions, Decimals & %'s Challenge
by G R Burgin
Solution to Challenge # 2
What number am I?
I am a four digit number (ABCD).
My thousands digit (A) is 5 less than 1/6 of the number represented by my hundreds & tens digits (BC).
A = 1/6*(BC) - 5
My hundreds digit (B) is 1.8 more than 0.025 of the number represented by my tens & units digits (CD).
B = 0.025*(CD) +1.8
My tens digit (C) is 2 less than 125% of my units digit (D).
C = 125%*(D) – 2
What number am I?
Sometimes it is easier to solve a problem from back-to-front or bottom-to-top. Lets’ start with the tens digit (C):
C = (1.25 * D) - 2 , letting D equal to 0 through 9, we find that D can only be equal to either 4 or 8 in order to obtain a positive whole number for C (3 or 8).
B = (0.025 * CD) +1.8 and since CD can only equal 34 or 88,
Testing for CD = 34: B = (0.025 * 34) + 1.8 = 2.65 (a non-solution)
Testing for CD = 88: B = (0.025 * 88) + 1.8 = 4 (a solution)
A = 1/6 (BC) - 5 and since BC now equals 48, A = (1/6 * 48) – 5 = 3
The number is: ABCD = 3488
Contact: mathspuzzles@gordonburgin.com
© G R Burgin 2009