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?

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(75887) (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?
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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
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Solve the system by any means you know to get:
p = 4 miles
I = 11 miles
L = 8 miles
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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)
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Cheers,
Stan H.

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