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Question 163677: Hi....I am having a really hard time with word problems. I am not sure how to make this into an equation. Please help!!!
Tom is twice as old as Jill. In 6 years, Tom will be half again as old as Jill. How old are Tom and Jill?
Thanks....Kathy Gafford
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! Kathy,
This is a typical age word problem. You will see lots of them in math courses.
Your Question:
Tom is twice as old as Jill. In 6 years, Tom will be half again as old as Jill. How old are Tom and Jill?
The question does not give us Jill's age. I will use J to represent Jill.
You could use any letter but J is easier to connect with Jill.
So, let J = Jill.
Tom is twice as old as Jill.
So, let Tom = 2 times J or simply 2J
We are now going into the future exactly 6 years.
This means they both will be 6 years older.
Do you agree?
Jill's age 6 years from now = J + 6
Tom's age 6 years from now = (1/2)(J)
We equate J + 6 = 2J + (1/2)(J) and solve for J.
By the way, we can write (1/2)(J) as J/2...they both mean the same thing.
Back to your question.
J + 2 = 2J + J/2
We want to remove the fraction J/2. It's easier working without fractions.
To do so, multiply each term on both sides of the equation by 2.
2 times (J + 2) = 2J times(2) + 2 times(J/2)
We now have this:
2J + 12 = 4J + J
2J + 12 = 5J
12 = 5J - 2J
12 = 3J
12/3 = J
4 = J
At the beginning, I said that J = Jill's age.
So, Jill is 4 years old.
I also said that Tom's age is 2J.
So, Tom's age = 2(4) or 8 years old.
Did you follow?
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