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University/College
Fig:
I got an 83 (A B. On the low end, but still a B) on my first test this semester. I'm okay that I did better than I thought I was going to do (didn't miss a single question that simply had the equations there) but I didn't get a single one of the four word problems right. I got partial credit because I was able to figure out some of the problems so it's better than nothing but I'm still disappointed I couldn't figure them out.
Carl-E:
So... what were they? Some post game analysis can help you in the long run.
Fig:
1. Three times the lesser of two consecutive even number is 14 more than 2 times the greater even number. What are the numbers?
-I almost got this one right but I goofed up and put the same expression on both sides of the equation instead of leaving it on one side. So instead of the equation being 3x=14+2(x+2), which is the correct one, I ended up with 3x+x+2=14+(x+2). I got partial credit since I at least stuck with my incorrect formula all the way through and showed that it worked, but it was still wrong.
2. To pass your math class, you must obtain a grade of 70% of the total points possible. The points can be earned through the following: Six tests worth 100 points each, various online assignments totaling 235 points, and one final worth 200 points. If a studen wishes to skip all the online assignments, what is the minimum test and final percentage average that must be obtained to receive a passing grade? Two parts: A. Write the inequality that would model this scenario and B. Solve the inequality.
-The most I got with this was 'something' ≥ .70(1035).
3. The prediction of the total points in the Sixers-Nuggets game is between 187 and 197. Write an inequality that shows this, then, convert the inequality into an absolute value inequality (answer must include the absolute value symbol) that represents this prediction.
-I got the inequality 187≤x≤197, but I could not remember how to convert it to the equation.
4. Joe sells peanuts and cashews. He wants to make a 15lb mixture of peanuts and cashews that will sell for $6.80/lb. Peanuts cost $3.00/lb and cashews cost $9.00/lb. How many pounds of each must he have to make the mixture?
-I gave up on this one.
Loki:
4. Economically speaking, Joe should just put a very small amount of cashews in so that he actually has a profit margin :D
Okay, for serious now.
You are looking for two unknowns, lets call them p (the weight of peanuts in lb) and c (the weight of cashews in lb).
You want that together they are 15lb, because that's what the mixture is supposed to weigh. So:
--- Code: ---p + c = 15
--- End code ---
You also want the cost match certain criteria. The cost of the mixture will be 6.80/lb. So you could, for example, calculate how much the whole mixture will cost.
--- Code: ---15 * 6,80 = x (too lazy to punch it into a calculator)
--- End code ---
You also want to have part of them peanuts and the other part cashews. So you want that the cost is distributed between them.
--- Code: ---x = 3.00 * p + 9.00 * c
--- End code ---
Now you have two unknowns and two equations:
--- Code: ---p + c = 15
3.00 * p + 9.00 * c = 15 * 6.80
--- End code ---
You can now solve this using the methods known to you. For example, you could put the p on one side of the first equation and put the other side into the place where p occurs in the second equation.
Carl-E:
OK, reverse order established, I'll take on #3.
187 < x < 197 as an absolute value inequality. Recall that
|anything| < a
means
-a < anything < a
so we need to get the expression between two values that are negatives of each other. If find the value halfway between 187 and 197, we can use that as a center, (187 + 197)/2 = 384/2 = 192. Subtract this from all three sides of the original inequality, and you get
-5 < x - 192 < 5
which can be rewritten as
|x - 192| < 5
By the way, I tend to thing "between" means strictly between, which is why I used < instead of <. Some use it inclusively, if your instructor didn't accept both I'd mention it.
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