Ray and Paul have 17 marbles. Ray and Paul have 15 marbles. Neil and Paul have 14 marbles.How many do they have all together?

Question

I am trying to find out the answer to how many marbles each person has

Answer 1

I assume the second sentence should be "Ray and Neil have 15 marbles."

 

Let R = The number of marbles that Ray has

Let P = the number of marbles that Paul has

Let N = the number of marbles that Neil has

 

We have 3 unknowns, so we need three equations relating the unknowns.

1. Ray and Paul have 17 marbles  R + P = 17
2. Ray and Neil have 15 marbles   R + N = 15
3. Neil and Paul have 14 marbles  N + P = 14

 

Let's re-arrange equations 2 and 3:

R + N = 15                                     [Equation 2]

N = 15 - R                                      [Subtracted R from both sides]

 

N + P = 14                                     [Equation 3]

P = 14 - N                                      [Subtracted N from both sides

P = 14 - (15 - R) = R - 1                  [Substituted 15-R in place of N]

 

Now we can eliminate P from equation 1 and solve for R:

R + P = 17                                     [Equation 1]

R + (R-1) = 17                               [Substituted R-1 in place of P]

2R = 18

R=9

 

Solve for N:

N = 15 - R                                    [Re-arranged equation 2]

N = 15 - 9                                    [R=9]

N = 6

 

Solve for P:

P = R - 1                                      [Re-arranged equation 3]

P = 9 - 1                                       [R = 9]

P = 8

 

Check:

Ray and Paul have 17 marbles    9 + 8 = 17  (check)
Ray and Neil have 15 marbles    9 + 6 = 15  (check)
Neil and Paul have 14 marbles    6 + 8 = 14  (check)