Solutions by simplifying first

Let's continue using algebra as our method for solving equations. This time, we will take one more step than last time. The problems in this section should still be sufficiently simple enough to do without algebra. Yet that's why we'll use them--algebra should make simple sense.

Take a look.

Problem	Jack and Jill bought some trees at the "all trees are the same price" sale. Jack found four trees to buy while Jill found five. Their total with tax came to $420.03. How much was each tree with tax?
"Intuitive" solution	"Jack and Jill together bought nine trees. They spent $420.03 for all nine trees. So dividing $420.03 by 9 will give the price per tree. $420.03 ÷ 9 trees = $46.67 per tree. "
"Algebra" Solution	Algebra Reasoning Let p = the price per tree in $. We must define the variable. Since Jack bought 4 and Jill bought 5 with the total being $420.03. Simplifying common terms. Dividing both sides to "undo" the multiply by 9. Simplifying

Note that this process is nearly identical as what we did in the last lesson. The only difference is that now we have one small step of "simplifying" before applying an "undo" step.

Remember to always follow the 3 basic guidelines for a good solution:

• the problem situation explained: the defining of the variable and the writing of the first equation accomplish this.
• clear, easy to follow reasoning: showing your steps does this.
• the correct answer in correct units: verify your answer makes sense in terms of your variable's definition.
  Like in our example with Jack and Jill, "d = 46.67" means "the price per tree in $ is 46.67" - read our definition of d and you'll agree!

You will practice writing more of these solutions in your assignment. I have included more examples of this process in the assignment to help you get a great idea on how to do fabulous work.

Hint: If your handy with tables, you might like to uset them to help organize your solutions. (That's how I did mine.)