Literally Removing Both Squares

Logic Level 1

$\large \dfrac{ 1{{\square}} }{{{\square}} 4} = \dfrac14$

In the ratio above (of two 2-digit integers), both squares contain the same digit. Using that same digit, find

$\large \dfrac{ 2{{\square}} }{{{\square}} 5} .$

\frac15

\frac25

\frac35

\frac45

1 solution

Zee Ell
Oct 16, 2016

If our missing digit is $x$ , then by setting up the equation ,

$\frac { \overline {1x} }{ \overline {x4} } = \frac {10+x}{10x+4} = \frac {1}{4}$

$4(10+x) = 10x + 4$

$40 + 4x = 10x + 4$

$36 = 6x$

$x = 6$

Hence, our answer is:

$\frac {26}{65} = \dfrac{2\times13}{5\times13} = \dfrac{2\times\cancel{13}}{5\times\cancel{13}} = \boxed { \frac {2}{5} }$

Find the missing digit by using an equation is a far better method than trial-error.

Soha Farhin Pine Pine - 4 years, 7 months ago