Question

If the lesser of two consecutive even integers is five more than half the greater, what are the two integers?

Answer 1

let us say first(lesser) even integer is x

so that our next(greater) consecutive integer will be x+2

Framing expressions from given information:

the lesser of two consecutive even integers is five more than half the greater

half the greater here means (x+2) / 2

framing equation:

`x= (x+2)/(2) +5`

subtracting (x+2)/2 from left side, to bring common terms together:

`x-(x+2)/(2) =5`

finding lcd

lcd of 2 and 1 is 1, so converting both denominators into lcd ,

`(2x)/(2) - (x+2)/(2) = 5`

`(2x-x-2)/(2) =5`

`(x-2)/(2) =5`

cross multiplying

`x-2=10`

taking -2 on right and adding

`x=10+2`

Answer x=12 and x+2=14

So lesser even integer is 12 and greater is 14