Required to divide 45 into four parts, so that the first part with two added, the second with two subtracted, the third divided by two, the fourth multiplied by two, shall equal each other.

ups, sorry i did not put the general solution:
here it is:
1)a+b+c+d= 45
2)a+2=z–>a=-2+z
3)b-2=z–>b=2+z
4)c/2=z–>c=2z
5)d*2=z–>d=z/2
so: substitute 2,3,4,5 in 1–> -2+z+2+z+2z+z/2=45–>9/2(z)=45–>z=10
now substitute z=10 in 2,3,4,5 and you get 8,12,20,5.

I wasn’t sure how to do it mathematically, but I tired anyway.
a+b+c+d=45
a+2=b-2=c/2=d*2
a+b+d*4+d=45
a+b+5d=45
b-4+b+5d=45
2b+5d=49
This made it a little easier. I still had to guess and check back with a and c, though. This is what I got:
a=8
b=12
c=20
d=5

I broke each number into ‘component units’, knowing the final values will have to be equal (1 unit being defined as the unknown final value. Number 3 contained 2 component units, since it would be halved to reach the final value. Number 4 contained half a component unit, since it would be doubled to equal one of them. Numbers 1 and 2 equal one each, since their sum is two units. So there are a total of 4.5 component units, and the sum of all units must equal 45. 45 / 4.5 = 10, conveniently enough…and the individual answers can be found easily from here.

Start with 8, add 2 to get 10, and then find the remaining numbers using 10 as a base. 12-2=10 means 12 is the second, 20/2=10 means 20 is the third, and 5*2=10 means 5 is the fourth.

Equations:
a + b + c + d = 45
a+2 = b-2 = c*2 = d/2

Assumptions:
a and b are exactly 4 units apart
c is MUCH smaller than d
since the final versions of c and d must be equal, d cannot be odd (to prevent being divided into a fraction, which would cause problems for c)

I would say that section 1 would have to be 8, section 2 would be 12, section 3 would be 20 & section 4 would be 5. Each of these given their rules give the common number of 10.

suineg| Guest September 8th, 2007 - 10:36 ami think one answer is: 8, 12, 20, 5. Explanation:

1) 8+12+20+5=45

2) 8+ 2=10

3)12-2=10

4)20/2=10

5)5*2=10

suineg| Guest September 8th, 2007 - 10:48 amups, sorry i did not put the general solution:

here it is:

1)a+b+c+d= 45

2)a+2=z–>a=-2+z

3)b-2=z–>b=2+z

4)c/2=z–>c=2z

5)d*2=z–>d=z/2

so: substitute 2,3,4,5 in 1–> -2+z+2+z+2z+z/2=45–>9/2(z)=45–>z=10

now substitute z=10 in 2,3,4,5 and you get 8,12,20,5.

Joe| Guest September 8th, 2007 - 12:52 pmI wasn’t sure how to do it mathematically, but I tired anyway.

a+b+c+d=45

a+2=b-2=c/2=d*2

a+b+d*4+d=45

a+b+5d=45

b-4+b+5d=45

2b+5d=49

This made it a little easier. I still had to guess and check back with a and c, though. This is what I got:

a=8

b=12

c=20

d=5

Daniel| Guest September 8th, 2007 - 2:20 pm8, 12, 20, and 5, respectively.

8 + 2 = 12 – 2 = 20 / 2 = 5 * 2 = 10.

8 + 12 + 20 + 5 = 45.

How I solved this:

I broke each number into ‘component units’, knowing the final values will have to be equal (1 unit being defined as the unknown final value. Number 3 contained 2 component units, since it would be halved to reach the final value. Number 4 contained half a component unit, since it would be doubled to equal one of them. Numbers 1 and 2 equal one each, since their sum is two units. So there are a total of 4.5 component units, and the sum of all units must equal 45. 45 / 4.5 = 10, conveniently enough…and the individual answers can be found easily from here.

Bob| Guest September 8th, 2007 - 2:30 pm20+5+12+8 = 45

20/2= 10

5*2 = 10

&

12-2 = 10

8+2 = 10

Michael| Guest September 9th, 2007 - 1:35 amFirst to fourth, respectively: 8, 12, 20, 5

Hasan| Guest September 9th, 2007 - 4:45 amnumbers are 8,12,20,5

8+2=10

12-2=10

20/2=10

5*2=10

Elizabeth| Guest September 9th, 2007 - 10:28 am8+12+20+5=45

8+2=10, 12-2+10, 20/2=10, 5×2=10

Sanjay| Guest September 9th, 2007 - 9:14 pmP1 = 8, P2 = 12, P3 = 20, P4 = 5

So P1 + P2 + P3 + P4 = 45 and

P1 + 2 = P2 – 2 = P3/2 = P4 x 2 = 10

John Lewis Highsmith| Guest September 9th, 2007 - 11:48 pmThe values are 8, 12, 20, and 5.

Nayan Shah| Guest September 10th, 2007 - 4:31 amThe four parts are : 8,12,20,5

8+2=10

12-2=10

20/2=10

5*2=10

Tania| Guest September 10th, 2007 - 6:44 am8 +2

12 -2

5 x 2

20 / 2

think| Guest September 10th, 2007 - 7:16 am8+12+20+5 = 45

8+2 = 10

12-2=10

20/2=10

5*2=10

Start with 8, add 2 to get 10, and then find the remaining numbers using 10 as a base. 12-2=10 means 12 is the second, 20/2=10 means 20 is the third, and 5*2=10 means 5 is the fourth.

Now add then together and you get 45.

Slavco| Guest September 10th, 2007 - 7:56 amFirst part: 8

Second part: 12

Third part: 20

Fourth part: 5

8+12+20+5=45

(8+2)=(12-2)=(20/2)=(5*2) = 10

jason| Guest September 10th, 2007 - 8:19 am8,12,20,5

Shawn| Guest September 10th, 2007 - 9:04 am8 + 2 =10

12 – 2 = 10

20 / 2 = 10

5 x 2 = 10

8 + 12 + 20 + 5 = 45

JasonJ| Guest September 10th, 2007 - 1:15 pmPart 1 + Part 2 + Part 3 + Part 4 = 45

8 + 12 + 20 + 5 = 45

Part 1: 8+2=10

Part 2: 12-2=10

Part 3: 20/2=10

Part 4: 5*2=10

ben Laidlaw| Guest September 10th, 2007 - 1:16 pm8 12 20 5

Mudit| Guest September 10th, 2007 - 1:19 pmVariables: a, b, c, d

Equations:

a + b + c + d = 45

a+2 = b-2 = c*2 = d/2

Assumptions:

a and b are exactly 4 units apart

c is MUCH smaller than d

since the final versions of c and d must be equal, d cannot be odd (to prevent being divided into a fraction, which would cause problems for c)

Answer:

a = 8

b = 12

c = 5

d = 20

andrew| Guest September 10th, 2007 - 4:10 pm1st part = 8

2nd part = 12

3rd part = 20

4th part = 5

andi| Guest September 10th, 2007 - 7:52 pm8,12,20,5. I don’t know how I figured it out. I just “saw” it. Sorry.

Oakenempty| Guest September 10th, 2007 - 8:20 pmI would say that section 1 would have to be 8, section 2 would be 12, section 3 would be 20 & section 4 would be 5. Each of these given their rules give the common number of 10.

ken| Guest September 10th, 2007 - 10:28 pm8, 12, 20, 5

RK| Profile September 10th, 2007 - 10:38 pmAnswer: 8, 12, 20, 5

lots of good explanations given above!

paul| Guest October 29th, 2007 - 7:23 amthe answer is 11.25