Algebra 1 Word Problems - Quantity
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How Many
Word Problems - Quantity

 
 You may see problems that look like this:
 
 Joe has 4 dollars more than Fred.
 Between them, they have 10 dollars.
 How much does each have?
 
 Here's how it works.
 We're going to call the number of dollars one of them has X.
 
 Which one.
 
 Well, you could use either one,
 but generally in the problem it says something like:
 "as Fred" or "than Joe."
 That's who gets to be X.
 In our problem, it says "than Fred"
 So...

 Fred (actually Fred's dollars) gets to be X.

 
 The problem also says:
 "Joe has 4 dollars more than Fred."
 That means:

 Joe has X + 4 dollars.

 
 The problem also says:
 "Between them, they have 10 dollars."
 That means:
 

 Joe's dollars + Fred's dollars = 10 dollars

 
 "Fred's dollars" is X.

"Joe's dollars" is X + 4 

 So ...

 X + X + 4 = 10

 
 and we've done stuff like that before.
 

 
 We said that X was Fred's dollars,
 and X + 4 was Joe's dollars,
 so ...

 Fred has 3 dollars.

Joe has 3 + 4 = 7 dollars.

 
 Here's another one.
 
 Example:
 
 Leslie, Chris, and Shawn all collect dinosaur eggs.
 
 Leslie has five times as many dinosaur eggs as Chris.
 Shawn has one dinosaur egg less than Chris.
 Together, they have 27 dinosaur eggs.
 How many does each one have?
 
 OK, in this one we have both "as Chris" AND "than Chris"
 so ...

Chris gets to be X.

 
 OK, it's actually Chris' dinosaur eggs 
 that get to be X.
 
 The problem says:
 "Leslie has five times as many dinosaur eggs as Chris"
 so ...

Leslie has 5 times X (also known as 5X).

 
 The problem also says:
 "Shawn has one dinosaur egg less than Chris"
 so ...

Shawn has X - 1

 
 Together they have:

27 dinosaur eggs

 
 Chris' dinosaur eggs + Leslie's dinosaur eggs +
 Shawn's dinosaur eggs = 27
 so ...

 

 
 Chris was X so
 Chris has 4 dinosaur eggs.
 Shawn has X - 1 so
 Shawn has 3 dinosaur eggs
 Leslie has 5X so
 Leslie has 20 dinosaur eggs.
 

   copyright 2005 Bruce Kirkpatrick

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