Ruth is twice as old as Pat. In 4 years ruth will be three times as old as Pat was 3 years ago. How old is each now?
R = 2 P
R + 4 = 3 (P - 3)
substituting ... 2 P + 4 = 3 P - 9
To solve this problem, let's start by assigning variables to the ages of Ruth and Pat.
Let's say Ruth's current age is R, and Pat's current age is P.
Based on the information given in the question, we can form two equations:
Equation 1: "Ruth is twice as old as Pat"
R = 2P
Equation 2: "In 4 years, Ruth will be three times as old as Pat was 3 years ago"
(R + 4) = 3(P - 3)
Now, we have a system of two equations with two variables. We can solve this system of equations to find the values of R and P.
Let's solve the first equation for R:
R = 2P
Substitute this value of R into the second equation:
(2P + 4) = 3(P - 3)
Now, solve for P:
2P + 4 = 3P - 9
Combine like terms:
9 = P - 4
Add 4 to both sides:
13 = P
So, Pat's current age is 13.
Now, substitute this value of P into the first equation to find Ruth's age:
R = 2P
R = 2(13)
R = 26
Therefore, Ruth is currently 26 years old, and Pat is currently 13 years old.