# SOLUTION: Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 miles, how far did each of them run?

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 Click here to see ALL problems on Numbers Word Problems Question 174226: Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 miles, how far did each of them run?Answer by stanbon(57347)   (Show Source): You can put this solution on YOUR website!Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 miles, how far did each of them run? ------------- Equations: p = (1/2) L p = I - 7 p + I + L = 23 ----------------- Rearrange: p + 0 - (1/2)L = 0 p - I + 0 = -7 p + I + L = 23 --------------------- Solve the system by any means you know to get: p = 4 miles I = 11 miles L = 8 miles ========================= Another way to find the solution: Equations: p = (1/2) L p = I - 7 p + I + L = 23 --------------- Rearrange to get: L = 2p I = p+7 Equations: p = (1/2) L p = I - 7 p + I + L = 23 ---- Substitute into p + I + L = 23 to get: p + p+7 + 2p = 23 4x + 7 = 23 4x = 16 p = 4 miles (paul) L= 2p = 8 miles (Lucy) I= p + 7 = 4+7 = 11 miles (Isaac) --------------------------------------- Cheers, Stan H.