Question 844835: jack is twice as old as his sister tia together their ages add up to 21 how old are the two children?
Answer by pmesler(52)   (Show Source):
You can put this solution on YOUR website! When doing word problems, the first thing to do is translate the sentence into a mathematical statement. When we don't know what a certain quantity or number is, we usually say it is x. In this problem we know that Jack is twice is old as his sister and together their ages add up to 21, but we still don't know what their individual ages are. Since we don't know what their ages are let's say that Jack's age is 2x and his sister's is x. Why is this? Well we don't know what their ages are but we know that Jack's age is twice his sister's. Whenever we see "twice" something we automatically know that we are doubling some unknown quantity, in this case x, and we write it as 2x. Therefore
2x = Jack's age.
x = Jack's sister's age.
The next part of the problem tells us that "together their ages add up to 21." When we see "add up" that obviously means we add the two expressions. Therefore we can write the problem like this:
2x+x = 21.
Now all we need to do is solve for x.
First let's add the x terms. When we do this we get
3x = 21. Now we divide each side of the equation by 3 and we get
x = 7.
Remember that x is Jack's sister's age. Therefore she is 7 years old.
Jack's age is 2x or 2(7) = 14. Therefore Jack is 14 years old.
|
|
|
