Algebra help, anyone?!?

Question

1.) The perimeter of a certain square is 8in. George needs to photocopy the square. He hopes to make a copy that is percisely the same size as the original. However, after making his copy, George discovers that the photocopier triples the length of every line. How many times larger than the original square is the photocopied square?
6 maybe? i dont know

2.) The players on a baseball team each have different numbers on their uniforms. Each uniform number is divisible by 2, divisible by 3, or divisible by both 2 and 3. Fifteen players have uniform numbers that are divisible by 2. 12 players have uniform numbers that are divisble by 3. 6 players have uniform numbers that are divisible by both 2 and 3. How many players are there on the baseball team?

3.) There are 363 students at Meadowbrook High School. There are 10 more freshmen than sophomores, 20 more juniors than sophomores, and 7 more seniors than freshmen. How many seniors are there at the school?

Please show me how too!

Answer 1

1: Perimeter of square = 8
Each side = 8 / 4 = 2
Photocopier multiplies sides by 3
New side = 2*3 = 6
Area of new square = 6*6 = 36
Area of old square = 2*2 = 4
New square 36/4 or 9 times larger

2: 15 divisble by 2
12 divisible by 3
6 divisible by 2 and 3

Since 15 are divisible by 2 and 6 by both 2 and 3, 15-6 or 9 are only divisible by 2

Since 12 are divisible by 3 and 6 by both 2 and 3, 12-6 or 6 are only divisible by 3

Total players = Those ony divisible by 2 plus those only divisible by 3 plus those divisible by both 2 and 3
or 9 + 6 + 6 or 21

3: Let x be the number of sophomores
So there are 10+x freshman
and 20+x juniors
and 7+(10+x) seniors
Total students are x + (10+x) + (20+x) + (7+(10+x)) or
47 + 4x students
We know there are 363 students so
363 = 47 + 3x
363 - 47 = 3x
316 = 4x

x = 79
79 sophormores
89 freshmen
99 juniors
96 seniors

Answer 2

1. Since the perimeter of the square is 8, that means each side is 2 inches. Every side is triple the length of the original or 6 inches each side. If by larger you mean area, then it is 4 inches for the first one and 36 for the second one, 9 times bigger.
2. You just make a venn diagram. Make two circles overlapping, with an oval in between. It tells you that there are 6 players with both numbers. It then says that there are 15 players with the number 2. That means that only 9 players have just the number 2. Repeat the process with 12 players having only the number 3 and you get 6. Add the numbers 9, 6, and 6 and you get 21.
3. Based on the word choice you can write an equation like this. Freshmen = Sophomores + 10, Sophomores are the variable, Juniors = Sophomores + 20, and since Seniors are 7 more than Freshmen, Seniors = Sophomores + 17. Rewriting the equation and simplifying makes: 363 = 4So + 47. 316 = 4So So = 79 students. F = 79 + 10 J = 79 + 20 and S = 79 + 17 or there are 96 seniors.

Answer 3

With this question, you need to find the area of the orignal square, and the area of the new square and determine how much bigger the new square is.
You are given the perimeter of the first square.
Perimeter of a square = 4 * the side
If the perimeter is 8, and you want to have the side then:
8=4s
Divide by four.
2=s
The area of the first square then is A=s^2
A=2^2
A=4
The length of every line for the new square is tripled.
That's 2*3=6.
Find the area of the new square.
A=6^2
A=36.
36/4 = 9.
The new square is nine times larger than the old.

2) For this you need to draw a venn diagram.
Draw two circles that overlap. On the left, you can put the number of players with a number divisible by 2, the right will be numbers divisible by 3 and the middle is 2 and 3.
First start with the middle because that is where the circles overlap. There are 6 in the middle. So to find the left, you first have to subtract the six that is already in that circle and you get 9. Same on the other side you get 6. So 9 players have a number divisible by two ONLY, six have a number divisible by two and three, and 6 players have a number divisible by 3 ONLY.
So 6+6+9=21
21 players.

I don't feel like doing three.

Answer 4

1) 9 times

If the perimeter of the original square was 8, then the length of each side was 2. The area would be 2 * 2 = 4. Tripling each side gives a length of 6 for each side. Area would be 6 * 6 = 36. 36/4 = 9

2) 21

(15 - 6) + (12 - 6) + 6 = 21

Exclude the numbers that are divisible by both 2 and 3 from the first two groups. Then add 6.

In effect, you're adding:

# uni's divisible ONLY by 2 + #uni's divisible ONLY by 3 + #uni's divisible by BOTH 2 AND 3

3) 96

Think in terms of sophomores.

s = sophomores
s + 10 = freshmen
s + 20 = juniors
s + 17 = seniors

Add 'em up: s + s + 10 + s + 20 + s + 17 = 363

4s + 47 = 363
4s = 316
s = 79

There are 79 sophomores, so there are 96 seniors.

Answer 5

#3) sophomores = x ; x + (x+10) + (x+20) + (x + 17) = 363 so 4x + 47= 363, so 4x = 316, so x = 79 . there's 79 sophomores, then add 17( 10 + 7) to 79 and you have 96 seniors. EDIT - jesusfreak made an error, its 4x or 4s, not 3, I'm sure

Answer 6

You need to set up an equation.
for number 3:
x is sophomores
363= s+10+s+20+s+17 17 comes from 10 and 7
363=3s+47

You should be able to solve that. Good Luck! God Bless!

Answer 7

The first one is 9 times larger.

Answer 8

the answer for 2nd one is 21 and for the 3rd one is 96 seniors
SOLUTIONS:
3.) 4x+47=363 x= 76 17+x=96
2.) 15+12-6=21
n(AuB)=n(A)+n(B)-n(A^B)