SOLUTION: I can't figure out the following equation: Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 MI, how far did each person run?

Question 175232This question is from textbook
: I can't figure out the following equation:
Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 MI, how far did each person run? This question is from textbook

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let x = number of miles paul jogged.
let y = number of miles lucy jogged.
let z = number of miles isaac jogged.
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paul jogged half as many miles as lucy:
x = .5y
solving for y, we get:
y = 2x
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paul jogged 7 miles less than isaac.
x = z-7
solving for z, we get:
z = x+7
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the total number of miles jogged is 23:
x + y + z = 23
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we can substitute 2x for y, and x+7 for z to get:
x + 2x + x + 7 = 23
combine like terms to get:
4x + 7 = 23
subtract 7 from both sides to get:
4x = 23 - 7 = 16
divide both sides by 4 to get:
x = 4
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now that we have x = 4, we can go back to the original equation and find the value of y and z.
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paul jogged 4 miles (x = number of miles paul jogged).
this means that lucy must have jogged 8 (y = 8) because 4 is 1/2 of 8.
this means that isaac must have jogged 11 (z = 11) because 4 is 11 minus 7.
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we have:
x + y + z = 23
substituting, we get:
4 + 8 + 11 = 23
which becomes:
23 = 23 proving the values for x,y,z are good.
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paul jogged 4 miles.
lucy jogged 8 miles.
isaac jogged 11 miles.
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