3.6+Two+Relative+Values

Section 3.6 - Two Unknown, Relative Values
There is a special group of story problems or application problems that seem trickier than they are because it seems like they don't give you enough information, or don't give you the information that you expect. Take this one for example:
 * Last Saturday, Josh earned $40 less than 3 times as much as Luke. Together they made $320 that day. How much did each man earn? **

There are actually two math equations hidden in this problem. Either one, alone, would not solve anything, but together they hold the key to the Holy Grail of math knowledge -- at least as far as Josh and Luke's pay for the day is concerned.

First, I'll indicate what the variables represent. J = Josh's pay, L = Luke's pay.

The first sentence looks like this: ** J = 3L - 40 ** (Josh earned 40 less than 3 times Luke)

The second sentence is: ** J + L = 320 ** (Together, or combined, they earned $320)

Now the magic part: Substitute what J is equal to (first sentence) for the J in the second sentence. The result: ** (3L - 40) + L = 320 **

Now it looks a lot like the "solve for x" problems in the previous section. Simplify to get 4L - 40 = 320. Isolate to get 4L = 360. Divide to get L = 90. That suggests that Luke earned $90 for the day. If Josh earned 3 times that, less $40, he made $230. If 230 + 90 = 320, we did it right.

__**Ex. Story #1**__ **Last night J and E together scored 96 points. J scored 20 more then E. How many did each score?** //**Two things we know about the problem: Together J & E equaled 96 points**// //**: E plus 20 equals J's total**// **J+E=96 <-** ** E+20=J ** ** E + 20 + E = 96** ** 2E + 20 = 96 ** **__-20__ __-20__**     **__2E__ = __76__** **2 2**    **  E = 38  ** __**Ex. Story #2**__ Some chick who sells jewelery, sold necklaces for $70, and rings for $30. She sold 4 times as many rings as necklaces, for a total gain of $570 //We know these facts about this problem:// **Some necklaces for $70** **Some rings for $30** **Total sale $570** **4 times as many rings as necklaces.** //In math terms this is how it translates into numbers:// **70n+30r=570** ** r=4n ** **(r=4n) //sub r for 4n, then distribute// ** **70n + 30r = 570** ** //distribute 30 into 4n --->//  70n + 30(4n) = 570 ** **70n + 120n = 570** **__190n__ = __570__** **190 190**     **  n = 3  ** __Ex Story #3__ I have a board that is 10 feet long. I need to cut the first third of it at 3 feet, the third piece needs to be one foot longer t hen the second. What do the other two pieces need to to be cut at? **10= 3 + x + x+1 ** **10 = 3+x+x+1** ** 10 = 2x + 4 ** **-4 = -4**      **__6__  = __2x__** **2 2**     ** 3=x A.K.A X=3 **


 * Chapter Three Practice Problems**

**Where to from here?**
3.1 Variables and Constants 3.2 Terms 3.3 Equations 3.4 Formulas 3.5 Solving for X 3.6 Two Unknown Relative Values Chapter Three Summary Chapter Three Homework