Much of this write up is an explanation of how to read the problem and pull the variable names and relevant information. If you know this part, please skip to the bold line below for the math work.
Let's start by taking the information we are given in the problem statement and assigning variable letters. Standard examples of variables used in math problems are "x" or "y" but they could be almost any letter such as "P" and "T".
In the problem statement we are told to use "P" to represent Patty's current age. We are also told that we will want to solve for Tom's age- we can assign "T" to represent Tom's age (it could be any letter but "T" is the best choice since Tom is the name of the person).
Now that we have our variables defined we need to read the problem and see if there is any other relevant information we will need. In the problem, "write an expression for Tom's age in 7 years," tells us that we will be looking at the age of Tom (T) seven (7) years from now. Think addition because we are looking at adding 7 years. In the statement, "Tom will be half as old as Patty," think of the fraction 1/2 (aka 1 divided by two).
So lets take all of the information we now and summarize it.
- P (Patty's current age) <- this is told to us in the problem statement
- T (Tom's age)
- +7 (aka 7 years from now)
- In 7 years T (Tom's age) will be 1/2 P (Patty's current age).
- This statement implies that T (Tom's age) will depend on P (Patty's current age). For the same reason we often see y(x) [aka "y is a function of x"] we can think of this as T(P) [aka "Tom's age is a function of Patty's current age']
- Therefore, we are looking for a function that starts out with T(P) =
- Don't be scared if you don't understand this is essentially the same as T=
Now that we have all the info, let's start doing actual math.
- In 7 years, Tom will be half as old as Patty
- Start by writing an expression for Patty's future age- adding 7 years to P (Patty's current age)
- (P + 7)
- We know that T (Tom's age) will be half (1/2) of that number
- Multiply Patty's future age (P + 7) by one-half (1/2)
OR you can think of it as dividing Patty's future age (P + 7) by 2
- Now put it all together! Tom's age (as a function of Patty's current age) will be half of Patty's future age (in 7 years)
- THE ANSWER IS
T(P) = (P + 7) / 2