School-Safe Puzzle Games

## ‘Math by Two’ Problem

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.

### 25 Comments to “‘Math by Two’ Problem”

1. suineg | Guest

i 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

2. suineg | Guest

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.

3. Joe | Guest

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

4. Daniel | Guest

8, 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.

5. Bob | Guest

20+5+12+8 = 45

20/2= 10
5*2 = 10

&

12-2 = 10
8+2 = 10

6. Michael | Guest

First to fourth, respectively: 8, 12, 20, 5

7. Hasan | Guest

numbers are 8,12,20,5

8+2=10

12-2=10

20/2=10

5*2=10

8. Elizabeth | Guest

8+12+20+5=45
8+2=10, 12-2+10, 20/2=10, 5×2=10

9. Sanjay | Guest

P1 = 8, P2 = 12, P3 = 20, P4 = 5

So P1 + P2 + P3 + P4 = 45 and

P1 + 2 = P2 – 2 = P3/2 = P4 x 2 = 10

10. John Lewis Highsmith | Guest

The values are 8, 12, 20, and 5.

11. Nayan Shah | Guest

The four parts are : 8,12,20,5
8+2=10
12-2=10
20/2=10
5*2=10

12. Tania | Guest

8 +2
12 -2
5 x 2
20 / 2

13. think | Guest

8+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.

14. Slavco | Guest

First 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

15. jason | Guest

8,12,20,5

16. Shawn | Guest

8 + 2 =10
12 – 2 = 10
20 / 2 = 10
5 x 2 = 10

8 + 12 + 20 + 5 = 45

17. JasonJ | Guest

Part 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

18. Mudit | Guest

Variables: 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)

a = 8
b = 12
c = 5
d = 20

19. andrew | Guest

1st part = 8
2nd part = 12
3rd part = 20
4th part = 5

20. andi | Guest

8,12,20,5. I don’t know how I figured it out. I just “saw” it. Sorry.

21. Oakenempty | Guest

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.

22. ken | Guest

8, 12, 20, 5

23. RK | Profile