Here is a fraction: x over blank (x/ )
The denominator of the fraction is 5 more than the numerator.
If 1 is added to the numerator and 2 is subtracted from the denominator, the fraction will become 4/5. Find the fraction.
need the answer explained
denominator: 5 more than x: x+5
current fraction: x/x+5
add 1 to the numerator: x + 1
subtract 2 from the denominator: x+5 -2 (which is x+3 because 5-2=3)
so the fraction is now x+1/x+3
the question says that this new fraction is equal to 4/5
so x+1/x+3 = 4/5
cross multiply across the equal sign: (x+1)(5) = (x+3)(4)
multiply out: 5x+5 = 4x+12
bring xs to the left and numbers to the right: 5x-4x = 12-5
now we know that x=7, so we can sub 7 into the original fraction given in the first two lines of the question: x/x+5
Sub in 7 anywhere that there is an x: 7/7+5
=7/12 is the fraction!