Answer to Problem of the Month for 11/2020

Can you determine the values of each politician from the 5 clues below?
In each clue the sum of the four polical figures is equal to the number on the right.

Disclaimer:
This is a math problem and the numbers are meaningless. If you must make this into a political problem, then think of the numbers as golf scores or popularity scores depending on your political affiliation. Or better yet, Click here for a Thanksgiving puzzle with the same answers and no politics.

Solution to the Problem:

Trump = 6
Biden = 8
Pence = 7
Harris = 11
Obama = 29

let A = Trump
let B = Biden
let C = Pence
let D = Harris
let E = Obama

Then set up five equations:

 
2A + B + C = 27   
C + B + D + A = 32   
D + E + 2C = 54    
2D + E + A = 57    
2E + B + C = 73

Then rearrange the equations with the similar letters underneath:

 
2A + B +  C           = 27
 A + B +  C +  D      = 32
         2C +  D +  E = 54
 A          + 2D +  E = 57
     B +  C      + 2E = 73

Since there are as many equations as variables (and none of the equations are equivalent), then there must be a solution.

You could eliminate one variable (say E) by solving one of the three equations with E in it (I chose the 4th equation):

E = 57 - A - 2D

Then substitute for E in the other equations. That would give you four equations with just 4 variables:

2A + B + C = 27
A + B + C + D = 32
2C + D + (57 - A - 2D) = 54
B + C + 2 (57 - A - 2D) = 73

Simplify and rearrange the variables to get:

 2A + B +  C           = 27
  A + B +  C +  D      = 32
 -A     + 2C -  D      = -3
-2A + B +  C - 4D      = -41

Now you can eliminate one of the other variables like D in the same manner.

Solve for D in one of the equations and then substitute that expression for D in the other three equations.

You will then have three equations with three variables.

Then continue until you have one equation with one variable and it will be solved.

Correctly solved by:

1. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
2. Veena Mg	Bangalore, Karnataka, India
3. Tyler Mack	Redlands Middle School, Grand Junction, Colorado
4. Mitchell Yerkes	Redlands Middle School, Grand Junction, Colorado
5. Ivy Joseph	Pune, Maharashtra, India
6. Katherine Grossman	Redlands Middle School, Grand Junction, Colorado
7. Cassidy Hunter	Delta High School, Delta, Colorado
8. Taylor Balding	Redlands Middle School, Grand Junction, Colorado
9. John Simmons	Memphis, Tennessee

November 2020 Problem of the Month

Correctly solved by:

November 2020
Problem of the Month