lucy ran twice as many miles as paul but 3 less than isaac t

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

Solution

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