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
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