algebra word problem!!!help me please...?

Question

One-fourth the middle integer of three consecutive even integers is 24 less than one half the sum of the other two.find the integers.

Answer 1

30, 32, 34

You know the integers have to be even. If you multiply any number by 2, you will always get an even number. So let the first integer be 2x. The next consecutive even integer is then 2x+2 and the next even integer after that is 2x+4.

One-fourth of the middle integer is (2x+2)/4 and 24 less than one-half of the sum of the other two is (2x+(2x+4))/2 - 24.

So the equation is:

(2x + 2) / 4 = (2x + (2x + 4)) / 2 - 24

Simplifying:

(2x + 2) / 4 = (4x + 4) / 2 - 24
(2x + 2) / 4 = 2x + 2 - 24
2x + 2 = 8x + 8 - 96
2x + 2 = 8x - 88
90 = 6x
15 = x

So the first integer is 2x = 2(15) = 30.
The second integer is 2x + 2 = 2(15) + 2 = 32.
The third integer is 2x + 4 = 2(15) + 4 = 34.

Answer 2

given: let x be the first even integer
x +2 be the 2nd consecutive even integer
x +4 be the 3rd consecutive even integer
lets analyze the given toform the correct equation:

one-fourth the middle integer is (1/4)(x+2) since the middle integer of the three is x +2
is means = ; therefore its (1/4)(x +2)=
24 less than one half the sum of the other two is (1/2)( x + x +4) -24

therefore the equation is:

(1/4)(x+2)=(1/2)(x+x+4) - 24
(1/4)(x+2)=(1/2)(2x+4) -24 combine similar terms x +x
x +2 = 2(2x +4) - (24)(4) multiply both sides of the equation by its LCD or LCM which is 4

x+2=4x +8 -96 distributive property and multiplying 24 and 4
x -4x=-2 +8 -96 transposition to combine all similar terms
-3x = -90
x = 30 multiply both sides of the equation by the multiplicative inverse of -3 which is -1/3

therefore the unknown integers are:

x =30
x +2 =32
x +4 =36

Answer 3

It's all in the translation:
Let x= middle integer, smaller is x-2, larger is x+2
1/4 (x) = 1/2 (x-2 + x+2) -24
1/4 x = 1/2 (2x) - 24
1/4 x = x - 24
Mutiply each side by 4 to eliminate the fraction:
x=4x-96
Add 96 fto both sides:
x + 96 = 4x
Subtract x from both sides
96=3x
Divide by 3
32=x
The three even numbers are 30, 32 and 34

Answer 4

ok.. first.. let the middle integer be called x

then the 3 consecutive even numbers are... (x-2), x, (x+2)

then translate the sentence...

1/4(x) is the "One-fourth the middle integer".. rewrite as x/4

(x-2)+(x+2) is "sum of the other two... or x-2+x+2 = 2x
taking half of this.. we get x

then x/4 = {[(x-2)+(x+2)]/2}-24
x/4 = x-24... (x-2+x+2)/2 = x
x = 4x-96
-3x = - 96
x = (-96)/(-3)
x = 32.... which is the middle integer

the one lower.. is x - 2 = 30
the one above is x + 2 = 34
so your integers are 30, 32, 34

I will leave the checking up to you to see if they work.

Answer 5

You have something in that problem wrong. The most two integers can sum to is 18 (9+9).

There is no integer that is 24 less than half that sum.

-Dio

Oops... I was reading it wrong. Give me a sec.

30 32 34

Answer 6

The integers are 30, 32, 34

Answer 7

equation would be 0.25(x+2)=0.5(x+x+4)-24
making it x+2=4x-96
x+90=4x
90=3x
30=x
so 1st interger is 30, 2nd is 32 and 3rd is 34.
1/4 of 32=8
and half of 30+34=32 and subtract 24 and you get 8=8 proving this the correct answer

Answer 8

smallest integer be x.
Thus ur eqn is : 0.25(x+2)=0.5(x+x+4)-24
0.25x+0.5=x+2-24
22.5=0.75x
Hence x=30

Answer 9

30, 32, 34

Let them be x-2, x, x+2
1/2(x-2+x+2)-24=1/4(x)
1/2*(2x)-24=1/4(x)
x-24=1/4(x)
x=1/4(x)+24
x=(x+96)/4
4x=x+96
3x=96
x=32

Answer 10

write it out:
1/4(m)= 1/2(x+y)-24

m= middle integer
x,y=other two integers

then you have to that system thing which I am wayyyyy to tired to do :) good luck