SOLUTION: one student is asked to divide a half of a number by 6 and other half by 4 and then to add the two quantities. Instead of doing so the student divides the given number by 5 .if the

Question 515276: one student is asked to divide a half of a number by 6 and other half by 4 and then to add the two quantities. Instead of doing so the student divides the given number by 5 .if the answer is 4 short of the correct answer then the actual answer is.
Found 2 solutions by josmiceli, Maths68:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let the number =
given:
What student was asked to do:

What student did:

-------

Multiply both sides by

The actual answer is:

check:

Which is short of answer
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Number = x
Half of the x = x/2
Other half = x/2
He had to divide a half of 'x' by 6 and other half by 4 and then add the two quantities
=(x/2/6)+(x/2/4)
=(x/2)*(1/6)+(x/2)*(1/4)
=x/12+x/8
Take LCM
=(2x+3x)/24
=5x/24 (This the correct answer)

But

He divided the 'x' by 5 and got the answer which was 4 shorter of the correct answer
=x/5 (wrong answer short of 4)
if we add the 4 in above equation then correct answer and wrong answer will be sam
=(x/5)+4
So
5x/24=(x/5)+4
5x/24-(x/5)=4
Take LCM
(5*(5x)-(24*x))/120=4
(25x-24x)/120=4
x/120=4
Multiply by 120 both sides
120*x/120=4*120
x=480
Number is 480

Check
======
What he suppose to do
=(240/6)+(240/4)
=40+60
=100
What he actually did
=480/5
=96 (which is 4 shorter than the actual answer)

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