If we put the numeral 1 at the beginning of a five digit number, making it a six digit number, we get a number three times smaller than if we put the numeral 1 at the end of the number. Find out the five digit number.
Answers
Answer:
If we put numeral 1 in front of the number, we get a number three times smaller, than if we put the numeral 1 behind this number. Using an easy equation: 3(x+100000) = 10x+1 we find out that the number is 42857.
Step-by-step explanation:
It is slower, but perhaps more fun.
First you write the equation like a long multiplication question:
1 a b c d e
x_______3
a b c d e 1
This is the logic:
e x 3 ends in 1. e must be 7 (7x3=21, carry the 2)
d x 3 ends in 7-2. d must be 5 (5x3=15, carry the 1)
c x 3 ends in 5-1. c must be 8 (8x3=24, carry the 2)
b x 3 ends in 8-2. b must be 2 (2x3=6, no carry)
a x 3 ends in 2. a must be 4 (4x3=12, carry the 1)
1 x 3 ends in 4-1. this is true.
______2
1 a b c d 7
x_______3
a b c d 7 1
_____1
1 a b c 5 7
x_______3
a b c 5 7 1
___2
1 a b 8 5 7
x_______3
a b 8 5 7 1
1 a 2 8 5 7
x_______3
a 2 8 5 7 1
1
1 4 2 8 5 7
x_______3
4 2 8 5 7 1