In the ambrose family the ages of the three children are three consecutive even integers . if the age of the youngest child is represented by x + 3 write an eaqation to represent the oldest child. if the sum of the ages is 42 write an equation and solve for x. how old is the oldest child

The ages are consecutive even numbers.
The youngest child is  (x+3) years old.
Every even number is 2 more than the one before it.
So the three ages are

           (x + 3),  (x + 5),  and  (x + 7).

Their sum is    x+3  +  x+5  +  x+7  =  3x + 15

But we're told that their sum is  42, so we can write

                                              3x + 15 = 42  <== the equation

Subtract 15 from each side:  3x         =  27

Divide each side by  3 :          x         =   9    <== the solution

So the three ages are  12,  14,  and  16.

The oldest child is  16  years old.

Ok here we go ..there are plenty of ways to solve such math problems but we will go for the smartest and easiest ..5x+2y=7  -2x+6y=9we rearrange them into the following ..by multiplying the 1st equation by 2 it becomes 10x + 4y = 14we rearrange it and so it becomes 10x = 14 - 4yas for the second equation we multiply it by 5 and rearrange it so it becomes as to the following ..-10x + 30y = 45rearranging so 10x = 30y -45now 10x equals both 14 - 4y and 30y -45so   14 - 4y = 30y -4531 = 26yy= 31/26 = 1.19 or around 1.2so by now we can calculate x easily as  -2x+6y=9so 2x = 6y -9 = 6 * 31/26 - 9 = -1.84  then x = - 0.92 or around -0.9best luck!