Philip P. answered • 04/23/14

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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.

*Ray and Paul have 17 marbles*R + P = 17*Ray and Neil have 15 marbles*R + N = 15*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)

Ray and Neil have 15 marbles 9 + 6 = 15 (check)

Neil and Paul have 14 marbles 6 + 8 = 14 (check)

Philip P.

Thank you, Jim.

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04/23/14

Jim S.

04/23/14