<p>I am going through my barron's math book, and I am stuck on sooooo many questions. SO I'm going to post my questions in this thread, and I think everyone else should post their math questions they are stuck on too. so some of us will get help and others will get practice.</p>
<p>So here is my first question:</p>
<p>Regular blend coffee that sells for $3.00 a pound is to be mixed with a premium blend of coffee that sells for $4.50 a pound to produce 30 pounds of coffee that sells for $4.00 a pound. How many pounds of regular coffee should be in the mixture?</p>
<p>I set up two equations. For each I used x=# of pounds of regular blend coffee and y=# of pounds of premium blend coffee.</p>
<p>you know that x + y = 30, because there must be 30 pounds of coffee.</p>
<p>The second equation is a little bit harder to get, as you have to take into account that the average price per pound of the final coffee is $4.</p>
<p>So.. You know that the total amount of money to produce 30 pounds of the coffee must be 3x + 4.5y because you have x pounds of regular coffee at $3 a pound and y pounds of premium coffee at $4.50 a pound. So, to get another equation, you must do [(3x+4.5y)/30] = 4 or 3x + 4.5y = 120. In order to take into account the 30 pounds of coffee. </p>
<p>Then, it becomes basic algebra, system of equations. x = 30 - y. Substitute. You get </p>
<p>$4.00 is between $3.00 and $4.50
On the number line 4 divides the segment
[3, 4.5] into two parts, left and right, their lengths respectively:
4 - 3 = 1
4.5 - 4 = .5
Their ratio is 2 : 1.</p>
<p>THE RULE sez:
Take the ingredients in the opposite ratio.
Why?</p>
<p>Let's name a final price (or concentration) after mixing a "new price".
If new price were smack in the middle of the segment,
($3 + $4.5)/2 = $3.75,
we would need to take equal amounts of each blend:
15lb of regular and 15lb of premium.
New price would be
($3 x 15 + $4.5 x 15) / 30 = ($3 + $4.5) / 2 = $3.75.</p>
<p>When we start moving new price closer to one end of the segment, we'll need to include more of that ingredient in the mix.
In other words, the closer new price gets to $4.50, (and farther from $3.00), the more of $4.50 blend (and less of $3.00) we need to put in the mix.</p>
<p>"Think extreme":
I we want new price to be $4.49, we'll have to put mostly $4.50 blend in the mix.
"Think analogy":
fulcrum of a see-saw.</p>
<p>BigB_85: I am not a "math genius", but i believe i can find the correct solution by the least convoluted means possible(for me atleast, and i'm not trying to find the shortest-cut even though i should.)</p>
<p>If you know that there line l, given by the equation y=x, you can determine the y magnitude of the point P, as it is at a right angle to the point (6,0), and lies on line l. Logically speaking it must be 6 since x and y to the same extent at the same time, from the same starting value of (0,0). After finding this particular magnitude, you now have points P and R, both of which lie on line K. Consequently, you can use these two points to determine the slope, and use point R as the intersection of the line with the x axis. With this information you can construct the formula for line k and substitute x=0 into the equation to determine the value for y.</p>
<p>I don't really understand how you found the coordinate points of P....could you elaborate about that? I understand how you got the x coordinate (6) since like you said, "it is at a right angle to the point (6,0)", but I'm not sure how you got the y-coordinate of P.</p>
<p>since it has the same x coordinate as the point (6,0), and lies on the line y=x you can assume its x value is 6. Then all you have to do is put it into the equation y=x ->y=6 so (6,6)</p>
<p>i don't understand that slope thing. i see it's much quicker and easier solution.
if i were, i would do this.
y=ax+b -> basic line function.
since the points are (6,6) (10,0), 6=ax+b
0=10a+b </p>
<p>a=-1.5 -> b=15
then function will be y=-1.5x+15. </p>
<p>then k will intersect y-axis at 15. (y(0)=-1.5*0 + 15)</p>
<p>I still don't understand how you get the y coordinate of P? Why would you plug 6, the x coordinate of whatever point (they don't give it a variable), into y = x (line L)?</p>
<p>@ gcf101</p>
<p>Would it be possible to elaborate? I don't understand what you did in post # 10</p>
<p>@ Tsenguun</p>
<p>When you plugged in the numbers and don't know how you ended up y=-1.5x + 15</p>
<p>To Bigb85: adrenalinefox got the y coordinate by logic. the slope of line y=x is 1/1. Therefore, for every 1 unit to the right the line moves up 1 unit. So 6 units to the right=6 units up. Thats the most basic way i can explain it.</p>
