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Farra subtracted 5 from a number and then divided by 4. Next, he subtracted 4 from the original number and then divided by 5. He got the same final answer both times. What was the original number?

 Jun 11, 2020
 #1
avatar+549 
+2

Set \(x \) as the original number.

Write out equations: 

 

\(\frac {x-5} {4} = \frac {x-4} {5}\)

 

Cross-multiply:

\((x-5)5=(x-4)4\)

 

Simplify to...

\(5x-25=4x-16\)

 

Solve the equation by subtracting \(4x\) from both sides:

\(x-25=-16\)

 

Then add \(25\) on both sides:

\(x=-16+25=9\)

 

So the final answer would be \(x=9\)

 Jun 11, 2020
 #2
avatar+1128 
0

we would make the equation (x-5)/4=(x-4)/5 and simplify it into 5x-25=4x-16 when we multiply both sides by 20 and subtract 4x from both sides to get x-25=-16 we then add 16 from both side to get x-9=0 and then we finnaly add 9 to both sides to get x=9

 Jun 11, 2020

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