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.

[Answers to show Monday]

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)


    Answer:
    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

    Answer: 8, 12, 20, 5


    lots of good explanations given above!


  24. paul | Guest

    the answer is 11.25


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