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If 40x represents a three-digit positive integer with a ones digit of x and 1x is a two-digit positive integer with a ones digit of x, what value of x makes the equation (40x)/(1x) = 31 true?

 Nov 17, 2020
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40x   and  be  written as  4*10^2  + 0*10 + x  =  400 + x

1x  can be written as    1*10  + x  =  10 + x

 

So we  have

 

[ 400 + x ] / ;[ 10 + x ] =  31     multiply both sides by 10 + x

 

400 + x  +  31 [ 10 + x ]    simplify

 

400 + x  = 310 + 31x

 

400 - 310  =  31x - x

 

90  = 30x  diivide  both sides  by 30

 

x = 3

 

Check   403 / 13 =  31

 

 

 

cool cool cool

 Nov 17, 2020

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