Math/logic puzzle help?

Just a few math/logic puzzles i have had trouble figuring out. 10 points for whoever figures out the most of them.





1.) Which is the odd one out?





4 15 9 12 5 8 30 18 24 10


A -B- C- D E- F- G- H- I- J





2.) scale 1 and 2 are balanced. how many cherries are needed to balance the 3rd scale?





A=apple b=banana c=cherry





1 A C C C = B B B


2 B C C = A


3 A B = ?





3.) which number replaces the ?


(i dont understand this one at all...)


C= camel E= elephant P= pig W= walrus





C E P P W = 19


C C E P C = 19


C E E W C = 15


P E P P W = 20


E P C C W = ?


19 15 18 22





4.)find the missing number


(this should be shaped like a body)


head = 14


left arm = ?


right arm = 42


torso = 5


left foot = 15


right foot = 20

Math/logic puzzle help?
Questions 2 and 3 are similar. You are given equations and need to solve for multiple variables.





Number 2:


First take the 2 sides of the scale and set them as equations with both sides being equal.


A + 3C = 3B


B + 2C = A


Then plug in B + 2C for A in the first equation.


B + 2C + 3C = 3B


Solve this equation for B in terms of C.


B + 5C = 3B


B = 2.5C


Then plug this back into the first equation.


A + 3C = 3(2.5C)


Solve this new equation for A in terms of C.


A = 4.5C


Then you have both A and B in terms of C and need to solve for C into the third equation.


A + B = ?C


Solve for this equation plugging your solution for A and B back in.


4.5C + 2.5 C = 7C


So you get that you need 7 cherries to balance the third scale.





The third question is very similar to this but it requires much more algebra since there are many more variables.





First set the first two equations equal to each other, since they both equal 19.


c + e +2p + w = 3c + e + p


You can solve for any variable you want here. I chose to do c first.


p + w = 2c


c = (p + w)/2


Then plug this into another equation. I put it into the third one since it has 2c in it, which will cancel out the 2 in the denominator.


2c + 2e + w = 15


Solve for any variable you want. I chose w.


p + 2w + 2e = 15


2w = 15 - p - 2e


w = 7.5 - 0.5p - e


Then we plug this into another equation. I put it into the fourth equation.


3p + e + 7.5 - 0.5 p - e = 20


Then solve for another variable. I solved for p.


3p + 7.5 - 0.5 p = 20


2.5p = 12.5


p = 5


Now we have p as an actual value, so we put that into a solution we have in terms of p. We have a p in our solution for c so plug it in there.


c = (p + w)/2


c = (5+w)/2


c = 2.5 + 0.5w


Then plug that into an equation. I put it into the first equation.


2.5 + 0.5w + e + 2(5) +w = 19


2.5 + 1.5 w + e + 10 = 19


1.5w + e = 6.5


e = 6.5 - 1.5w


Now put all of our solutions into the last equation and solve to get a value for w.


3p + e + w = 20


3(5) + (6.5 - 1.5w) + w = 20


15 + 6.5 - 0.5w = 20


-0.5w = -1.5


w = 3


Then take this and plug it into the last equation again with all the numerical values we have.


3p + e +w = 20


3(5) + e +3 = 20


18 + e = 20


e = 2


Now we have a value for all of the variables except c. So pick any equation you want and plug all of our numbers in to get c. I did the first equation.


c + e + 2p + w = 19


c + 2 + 2(5) + 3 = 19


c + 15 = 19


c = 4


The last thing we need to do is plug all of our numbers into the fifth equation to get our final answer.


e + p +2c + w = ?


2 + 5 + 2(4) + 3


2 + 5 + 8 + 3 = 18


So 18 is your final answer.





I'm not sure about the first one and I don't even understand the last question... what does it mean that it's shaped like a body?
Reply:1. B and C


2. CCCC


3. 19


4. 57