A couple of maths questions im stuck at?

Question

You may NOT use a calculator. Please help by explaining working as far as possible.

1) A special offer jar of marmilande contains 12.5% more than a standard jar. The special offer jar contains 450g of marmalade. How much does a standard jar contain?

2)Location A sells 1200 tickets in a raffel and a boy buys 15 of them.
Location B sells 1800 tickets of which the boy buys 20.
In which raffel has the boy a better chance of winning 1st prize.
Show CLEARLY all your working.

Final Q 3) A piece of wire 10cm long is bent to make a circle.

The circumference of the circle is equal to the length of the wire.
Show that the area of the circle is exactly 25/pie* square centimetres.

* Pie being the mathematical symbol equal to 3.14

Thank you for your time.

Answer 1

1. set up a ratio
100%/112.5% = x/450
x= 400 in standard jar

2. use long division
15/1200= about 1.3% of winning
20/1800= 1.1% chance
Location A better chance of winning

3. 2 Pi R = Circum
thus
2 Pi R = 10cm
Radius = 5/Pi

Area of A circle formula = Pi R Squared
(5/Pi) Squared X Pi = Area = 25/Pi

Answer 2

1) X + 12.5% = 450 12.5% is 1/8, so basically you have 9/8X on the left.

Divide 450 by 9/8, or multiply by 8/9, to get 400. All done without using a calculator. (the 9 and 450(9*50) cancel to make 50*8 = 400)

2) A = 15/1200 or 1/800; B = 20/1800 or 1/900. A is the better chance.

3) Circumference = pi(d) = 10cm or D = 10/pi, or R = 5/pi
We know that area = pi(r^2), so that is pi(25/pi^2), or 25pi.

Answer 3

1 Special offer jar = standard jar plus 12.5%
Therefore 450g = 112.5% = 9/8
450/9 = 50 x 8 =400g
2. A: 15/1200 x100 = 1.25%
B: 20/1800 x 100= 1.11%
Therefore better chance in A
3. Cant remember circles sorry!

Answer 4

For number 2 you don't need to do long division. You need to compare 15/1200 for raffle A with 20/1800 for raffle B. If you turn both of these fractions upside down, the answer will be the smaller result rather than the bigger.
1200/15 = 400/5 (dividing top and bottom by 3)
= 80.
1800/20 = 900/10 (dividing top and bottom by 2)
= 90.
The boy therefore has a better chance in raffle A.

Answer 5

a million. f(4) = a million/4 (4) - a million => a million-a million => 0 2. m=((y? - y?)/(x?-x?)) => ((8-(-4))/(4-2) => (12/2) => 6 => m = 6 3. y=kx => 4=k2 => 4/2=ok => 2=ok 4. y=mx+b => 4=4(0) + b => 4=b 5. y- y? = m(x - x?) => y-3 = 3(x - (-4)) => y-3 = 3x + 12 => y= 3x + 15 6. m=((y? - y?)/(x?-x?)) => ((-a million - 9)/(6-4)) => (-10/2) => (-5) y= mx + b => 9 = (-5)(4) + b => 9= -20 +b => 29 = b 7. horizontal line because of the fact no slope, so y=5 8. you're lacking the element that the line is going via, so i'm no longer able to remedy this one. 9. y = (-3x) + a million, (a million, ?) => m= ? **do away with the sign and turn the different way up** => y- y? = m(x - x?) => y - ? = ?(x-a million) => y - ?= ?x - ? => y = ?x +?

Answer 6

1) find 10%(divide by 10), 1% (divide by 100), and 0.5% (half 1%), of 450g. add these together to make 12.5% subtract that from 450. thts your answer.

sorry i dnt know the rest
hope that helps though

Answer 7

1.) 450= Standard Jar x 1.125
Standard jar = 450/1.125
Standard Jar= 400