SOLUTION: Pls provide formula: lucy ran twice as many miles as paul but 3 less than isaac. they ran total of 23 miles. how far did each run?

Question 257986: Pls provide formula: lucy ran twice as many miles as paul but 3 less than isaac. they ran total of 23 miles. how far did each run?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Let's break the problem down into its parts
"Lucy ran twice as many miles as Paul but 3 less than Isaac. They ran total of 23 miles. How far did each run?"
"Lucy ran"
Let L equal the miles Lucy ran
"twice as many miles as Paul"
Let P equal miles run by Paul
L=2P
"but 3 less than Isaac"
Let I equal miles run by Isaac
L=I-3
"They ran total of 23 miles."
L+P+I=23
So now we have three equation sin three unknowns. That is just what we need.
L=2P
L=I-3
L+P+I=23
How far did each run?
So we are asked for the values of L and P and I
We rearrange the first two equations.
We have L=2P
But we want P by itself
L=2P
divide both sides by 2
L/2=P
now the other one
L=I-3
add 3 to both sides
L+3=I
so now we have
P=L/2
and I=L+3
and L+P+I=23
so now we we substitute L+3 for I and L/2 for P
L+P+I=23
L+(L/2)+ (L+3)=23
Let's remove the parentheses
L+L/2+L+3=23
Let's combine
2L+L/2+3=23
subtract 3 from both sides
2L+L/2=20
multiply both sides by 2
4L+L=40
combine
5L=40
divide both sides by 5
L=8
We also want to solve for P and I
P=L/2=8/2=4
and I=L+3=*+3=11
L = 8 miles, P = 4 miles, I = 11 miles
check
L+P+I=23
8+4+11=23
ok

RELATED QUESTIONS
Lucy jogged twice as many miles as Paul but 3 less than Isaac.If the three ran a total of (answered by jorel1380)

Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a... (answered by stanbon)

I can't figure out the following equation: Paul jogged half as many miles (mi) as Lucy (answered by gonzo)

ethan ran two and a half times as far as conor. will ran 3 more miles than conor.... (answered by ankor@dixie-net.com)

Jeffery is training to run a marathon. On Monday he ran and walked a total of 11 miles.... (answered by tommyt3rd)

ethan ran two and a half times as far as conor. will ran 3 more miles than conor.... (answered by faceoff57)

Last week Paul ran 16 miles less than Jimmy. Paul run 11 miles. How many miles did Jimmy... (answered by EdenWolf)

Devon ran twice as far as Jovan. Altogether they ran 18 km. How many kilometers did each... (answered by ikleyn)

Eric is preparing to run in the Bay Marathon. One day, he ran and walked a total of 16... (answered by checkley75)