| 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 |
