Hillary has 3 times the amount of money as paul. Jeff has 4 less than Hillary and 5 more than paul. How much do they have each?

Question

Hillary has 3 times the amount of money as paul. Jeff has 4 less than Hillary and 5 more than paul. How much do they have?

Answer 1

Let the amount Paul has = P

Let the amount Jeff has = J

Let the amount Hillary has = H

 

We can set equations based on the problem description.

 

H = 3P             eq1

 

J = 3P - 4           eq2

 

J = P + 5           eq3

 

 

We have 3 equation with 3 different variables.   We want to reduced the number of equations by using substitution and elimination methods.

 

 

We can equate eq2 and eq3.  This will give us an equation in terms of P.

 

3P - 4 = P + 5

 

 

Subtract P on both sides of the equation.

 

2P - 4 = 5

 

 

Add 4 on both sides of the equation.

 

2P = 9

 

 

Divide both sides of the equation by 3.

 

P = 4.5

 

 

Next we substitute this value of P into eq2 or eq3 to find Jeff's amount.  Since eq2 and eq3 both represent Jeff's amount, we can pick either equation.  Lets pick eq3, since is more simpler to calculate.

 

J = 4.5 + 5

J = 9.5

 

 

Substitute the value of P once more to find Hillary's amount.

 

H = 3(4.5)

H = 13.5

 

 

 

Hillary has $13.50

Paul has  $4.50

Jeff has $9.50