Question

find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 742​

Answer 1

Answer:

The four consecutive even integers are:

⇛ 120, 122, 124, 126

Given:

➡ The sum of the first two added to twice the sum of the last two is equal to 742 of four consecutive even integers.

To Find:

The four consecutive even integers.

Solution:

We are given,

▪ The sum of the first two added to twice the sum of the last two is equal to 742 of four consecutive even integers.

Let the four even integers be a, a+2, a+4 and a+6 .

⛬ According to given condition,

➞ a + ( a + 2 ) + 2( a + 4 + a + 6 ) = 742

➞ a + ( a + 2 ) + 2a + 8 + 2a + 12 = 742

➞ 6a + 22 = 742

➞ 6a = 742 - 22

➞6a = 720

➞ a = 720 / 6

⛬ a = 120

Now the four consecutive even integers are :

➵ a = 120

➵a + 2 = 122

➵a + 4 = 124

➵a + 6 = 126

Answer 2

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ four \ consecutive \ even \ integers \ are}$

$\sf{120, \ 122, \ 124 \ and \ 126 \ respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{Their \ are \ four \ consecutive \ even}}$

$\sf{integers, \ the \ sum \ of \ the \ first \ two}$

$\sf{added \ to \ twice \ the \ sum \ of \ last \ two}$

$\sf{equal \ to \ 742.}$

$\sf\pink{To \ find:}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ four \ consecutive \ even \ integers}$

$\sf{be \ a-3, \ a-1, \ a+1 \ and \ a+3.}$

$\sf{According \ to \ the \ given \ condition}$

$\sf{(a-3+a-1)+2(a+1+a+3)=742}$

$\sf{\therefore{2a-4+2(2a+4)=742}}$

$\sf{\therefore{2a-4+4a+8=742}}$

$\sf{\therefore{6a+4=742}}$

$\sf{\therefore{6a=742-4}}$

$\sf{\therefore{6a=738}}$

$\sf{\therefore{a=\frac{738}{6}}}$

$\sf{\therefore{a=123}}$

$\sf{The \ four \ consecutive \ even \ integers \ are:}$

$\sf{\implies{a-3=123-3=120,}}$

$\sf{\implies{a-1=123-1=122,}}$

$\sf{\implies{a+1=123+1=124,}}$

$\sf{\implies{a+3d=123+3=126.}}$

$\sf\purple{\tt{\therefore{The \ four \ consecutive \ even \ integers \ are}}}$

$\sf\purple{\tt{120, \ 122, \ 124 \ and \ 126 \ respectively.}}$