CPhill

42 = 2 x 3 x 7

65 = 5 x 13

Notice that these two numbers have no common factors....thus nothing would "cancel".....so the fraction is in lowest terms......!!!

Call x the number of campers on the low trail and y the number of campers on the high trail.

So we have

x + y  ≤ 30

x ≥10

y ≥ 5

This has many solutions....(10, 20) (11, 19) (12, 18) ( 13, 17).....etc.......(24,6)  (25, 5)

We can graph this...but there will be many "solution" points that aren't whole numbers - and thus - aren't really a part of the solution set because we can't have "part" of a person !!!

Hang in there DS.......tomorrow....you might be at the top of the board......the "point" totals seem to fluctuate more than the Dow Jones Industrials !!!!!

I'm gong to do the "set-up" but I want YOU to do the solving trQ !!!  You have to learn how to do this and I did one earlier for you......

Let x be the price of each orange and y be the price of each grapefruit.  So we have....

8x + 1y =   4.60

6x + 3y =   4.80

Hint....think about multiplying the top equation by -3 and adding it to the second equation to "eliminate" y.....!!!

This system has a solution.....don't ask me how I know....I just do !!!!

Let me know if you get stuck and I'll talk you through it...this might seem painful....but you won't learn just by being an "observer"

Here's my two cents worth about this one:

This is a discontinuous function - and it passes the vetical line test because any vertical line would only cut the "graph" in one place. The graph would have an infinite number of disconnected "peaks" and "valleys" because the x values along the number line are continuous. In other words, all the rationals would have y values of 1 and all the irrationals would have values of 0. The graph is definitely non-continuous because there aren't any "intermediate"  y values - i.e., "y" is either 0 or 1 - and nothing in between !!   Basically, the graph would be just  "dots" at either y= 0 or at y =1. In a strange way though, this is an "even" function, because the negative of any positive rational would have a corresponding y value of 1 and the negative of any positive irrational would have a corresponding y value of 0. Thus, f(x) = f(-x). The y intercept would be  the "dot" at (0, 1) - because 0 is rational. The "x" intercepts would just be the "dots" where the irrational numbers are located on the number line because "f(x)" would be 0 at those points!!!  The domain is all real numbers, but there are onl two values for the "range" .....0 and 1 !!!

That's my "take" on this one !!!

You can put the fiirst one into the onsite calculator....for the second one, we have....

5c+1 = 7c - 8     add 8 to both sides

5c + 1 + 8  = 7c    subtract 5c from both sides

9 = 2c      divide both sides by 2

9/2 = c

Note, Anonymous.....if x were always equal to 1, the Algebra books would only be about 1/10 of their current thickness !!!! (LOL!!)

Sorry...I kinda' missed that minus sign....I went back and corrected my answer....thanks to NinjaDevo for bailing me out !!!

I assume you're OK with it, now???

What do you want to do??? Can you give us an example???

I believe ND made a slight mistake on this one.....let's multiply both sides by 12 right off the bat..this gives us...

8x + 3x = 17

11x = 17    divide both sides by 11

x = 17/11