Question

In two consecutive even numbers, 4/9 of the larger numbers is equal to half of the smaller number, find the numbers.​

Answer 1

Answer

We are given 2 consecutive even numbers.

Now let us see some consecutive even numbers

• 4,6
• 8,10
• 12,14

Now can we find any similarities among them

Yeah, : 6-4 = 10-8 = 14-12 = 2

(They have a difference of '2' )

Now if 'x' is an even number then its succeeding consecutive even number will be 'x+2'

Now as per the condition given,

$\implies \rm \frac { 4 } { 9 } (x+2) = \frac { x } { 2 }$

$\implies \rm \frac { 4x+8 } { 9 } = \frac { x } { 2 }$

Cross multiplying it

$\implies \rm 8x + 16 = 9x$

$\implies \boxed{\rm x = 16 }$

So,

$\implies \boxed{\rm x + 2 = 16 + 2 }$

$\implies \rm 18$

Hence the two consecutive even numbers are

ᗔ 16

ᗔ 18

Answer 2

$\bf\huge\underline{Answer}$

We are given 2 consecutive even numbers.Now let us see some consecutive even numbers -

${4,6}$

${8,10}$

$12,14$

Now can we find any similarities among them = $6-4 = 10-8 = 14-12 = 2$

(They have a difference of '2' )

Now if 'x' is an even number then its succeeding consecutive even number will be 'x+2.

$\bf\underline{Now \: as\: per\: the\: condition\: given,}$

$\implies\rm\frac{ 4 }{ 9 }(x+2)$ =$\frac { x } { 2 }$

$⟹94(x+2)=2x$

$\implies\rm\frac{ 4x+8 }{ 9 }$=$\frac{ x }$

${ 2 }⟹94x+8=2x$

$\bf\underline{Cross \:multiplying\: it}$

$\implies \rm 8x + 16 = 9x$

$⟹8x+16=9x$

$\implies \boxed{\rm x = 16 }$

$⟹x=16$

So,

$\rm{ x + 2 = 16 + 2 ⟹x+2=16+2}$

$\implies\rm 18⟹18$

$\bf\underline{Hence \:the\: two \:consecutive}$

$\bf\underline{even\: numbers\: are\: - }$

▪︎$16$

▪︎$18$