help please with explination
- the average ( arthematic mean ) of the test scores of a class of p students is 70 , and the average of the test scores of class n students is 92 . when the scores of both classes are combined , the average score is 86 what is the value of P\n ?
The sum of the test scores of the class of p students is 70p.
The sum of the test scores of the class of n students is 92n.
Adding these we get the sum of the test scores of both classes combined: 70p + 92n.
We can also get this sum directly from the problem: 86(p + n) = 86p + 86n.
So we have that 70p + 92n = 86p + 86n.
We get p to one side of the equation by subtracting 70p from each side, and we get n to the other side by subtracting 86n from each side.
6n = 16p
We can get p/n to one side by performing cross division. We do this just like cross multiplication, but we divide instead. Dividing each side of the equation by 16n will do the trick (this way we get rid of n on the left, and 16 on the right).
You can also solve those problems "visually" although it requires a bit of SAT math agility.
All one would do it "graph" the problem as such and show the intervals between the values and the final average. The reason this works is because of the logic that the group of students who score a 92 carry a weight and the students with 70 a different one. Those "weights" are inversely proportional to their "distance" from the average of 86. In so many words, the group of 92 carry a weight of 16 and the group of 70 a weight of 6. This weight, fwiw, is none other than the number of the students in the group.
The best here is to add those two equations, because there's 9x in the first equation and (-9x) in the second. Thus, adding them we get rid of x and find y:
-5*2-10*4+10*2+10*7+5*4-6y-6y=0
Also to simplify calculations let's factor out 10:
10(-1-4+2+7+2)=12y
10*6=12y
therefrom y=5
Now we can find x using either of two equations. Let's take the first one:
-5*2-10*4-6*5+9x=0
Putting 10 out front we get
10*(-1-4-3)=-9x
cancelling negative signs we obtain
10*8=9x
x=80/9
I had another question for math.
During a sale, for every three shirts purchased at regular price, a customer can buy a fourth at 50% off. If the regular price of a shirt is $4.50, and a customer spent $31.50 on shirts, how many shirts did the customer purchase?
The book explanation to me seemed to take too long.
This question comes from a PSAT practice test from PR ; I'm using the xiggi method -- at this point I'm taking it untimed and with answers.
Start by determining the price of a group of 4 shirts: 4.50 x 3 + 2.25 = 15.75. Just eyeballing it, 15.75 goes into 31.50 twice. The customer therefore bought two groups of four shirts or 8 shirts.
If the price for the 4 shirts didn't go into the total price evenly, you would divide the total price by the price of 4 shirts and then divide the remainder by the price of 1 shirt and add the totals (total shirts = #s of groups of 4 shirts times 4 plus the number of individual shirts).
I know that I'm really late but help would be must appreciated. I'm terrible at math so please don't judge : The smallest Integer of a set of even consecutive integers is -20. If the sum is of these integers is 72, how many integers are in this set? A) 20 21 C) 22 D) 23 E) 24
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- the average ( arthematic mean ) of the test scores of a class of p students is 70 , and the average of the test scores of class n students is 92 . when the scores of both classes are combined , the average score is 86 what is the value of P\n ?
The sum of the test scores of the class of p students is 70p.
The sum of the test scores of the class of n students is 92n.
Adding these we get the sum of the test scores of both classes combined: 70p + 92n.
We can also get this sum directly from the problem: 86(p + n) = 86p + 86n.
So we have that 70p + 92n = 86p + 86n.
We get p to one side of the equation by subtracting 70p from each side, and we get n to the other side by subtracting 86n from each side.
6n = 16p
We can get p/n to one side by performing cross division. We do this just like cross multiplication, but we divide instead. Dividing each side of the equation by 16n will do the trick (this way we get rid of n on the left, and 16 on the right).
p/n = 6/16 = 3/8.
So we can grid in 3/8 or .375.
All one would do it "graph" the problem as such and show the intervals between the values and the final average. The reason this works is because of the logic that the group of students who score a 92 carry a weight and the students with 70 a different one. Those "weights" are inversely proportional to their "distance" from the average of 86. In so many words, the group of 92 carry a weight of 16 and the group of 70 a weight of 6. This weight, fwiw, is none other than the number of the students in the group.
70
86
92
Delta => 16
6
The answer is 6/16!
Easy peasy!
-5*2-10*4-6y+9x=0
10*2+10*7+5*4-9x-6y=0
-5*2-10*4+10*2+10*7+5*4-6y-6y=0
Also to simplify calculations let's factor out 10:
10(-1-4+2+7+2)=12y
10*6=12y
therefrom y=5
Now we can find x using either of two equations. Let's take the first one:
-5*2-10*4-6*5+9x=0
Putting 10 out front we get
10*(-1-4-3)=-9x
cancelling negative signs we obtain
10*8=9x
x=80/9
Thus, the answer is 80/9, 5
During a sale, for every three shirts purchased at regular price, a customer can buy a fourth at 50% off. If the regular price of a shirt is $4.50, and a customer spent $31.50 on shirts, how many shirts did the customer purchase?
The book explanation to me seemed to take too long.
This question comes from a PSAT practice test from PR ; I'm using the xiggi method -- at this point I'm taking it untimed and with answers.
If the price for the 4 shirts didn't go into the total price evenly, you would divide the total price by the price of 4 shirts and then divide the remainder by the price of 1 shirt and add the totals (total shirts = #s of groups of 4 shirts times 4 plus the number of individual shirts).