It was 21st May ~ 521 (part 1)

Algebra Level 2

A B C D 1 A B C D = 5 21 \frac{\overline{ABCD}}{\overline{1ABCD}}=\frac{5}{21}

What is the value of the 4-digit number A B C D \overline{ABCD} satisfying the above condition?


The answer is 3125.

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1 solution

Zee Ell
May 21, 2017

Let x = A B C D 1 A B C D = 10000 + x \text {Let } x= \overline {ABCD} \Rightarrow \overline {1ABCD} = 10000 + x

x 10000 + x = 5 21 \frac {x}{10000 + x} = \frac {5}{21}

21 x = 5 ( 10000 + x ) 21x = 5(10000+x)

16 x = 50000 16x = 50000

x = 3125 x = \boxed {3125}

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