FOOD!

A typical large hamburger has 427 calories, 48% of them from fat. The same hamburger with cheese has 31g of fat, 53% of its calories coming from fat. Regular French fries have 220 calories in total and 12g of fat. A chocolate sundae has 360 calories and 28% of these calories come from fat.


Ed has a meal consisting of a typical large hamburger with double cheese, regular French fries and a chocolate sundae. What percentage of calories in the meal are fat calories?
(1g of fat has 9 calories

Hamburger

French Fries

Chocolate Sundae

Answer

Item	Total Cal	Grams Fat	Percentage Fat	Cal Fat
Hamburger	427	22.77	48	204.96
Burger + Cheese	526.42	31	53	279
French Fries	220	12	49	108
Choc. Sundae	360	11.2	28	100.8

1 Cheese	99.42	8.23	74.5	74.04
2 Cheese	198.83	16.45	74.5	148.08

Total

778.83

39.65

45.8%

356.88

Trigonometry - how 2 learn it quickly

How to remember trigonometry well:

A Right-Angled Triangle

Sin = opp/hyp

Cos = adj/hyp

Tan = opp/adj

Some Old Hag (SOH) 

Cracked All Her (CAH) 

Teeth On Alls (TOA)

This method is also very useful because the order of the sides is in order of how you divide them. (e.g. Some Old Hag - Sin = Opposite/ Hypotenuse)

A right-angled triangle with a line perpendicular to the hypotenuse

                                                                         

                                                                                               Y

A                                                                             X                                             B        

Question

Here is a right-angled triangle has an extra line descending from the original right angle, perpendicular to the hypotenuse.

If the hypotenuse (base) length is 7cm and if that extra line splits the base into 3cm and 4cm parts, what is the height of 'big' right-angled triangle?

Hint: (From nRICH)
Sometimes we use the word "scale" to mean enlarge or scale up - for another way to see this arrangement of right-angled triangles you may like to look at the problem called a Matter of Scale.




Answer

Scale Factor (*a)
BD = ab
AB = ac
AD = a^2 = 3


a = square root (3)


Scale Factor (*b)
DC = b^2 = 4 
BD = ab
BC = bc


b = square root (4)
b = 2


So: a * b
square root (3) * 2


= 2square root (3)
= 3.4641
BD = 3.46 (3.s.f)

Test Marks

Question
In a test consisting of 30 questions there were 5 marks for each correct answer, but a penalty of 3 marks for each wrong answer. Fred scored a total of 46 marks.
If you call the number of correct answers Fred wrote 'X,' write an equation involving 'X' and solve it.


Answer
30 questions


5X - 3(30-X) = 46
5X - 90 + 3x = 46


8X = 136
X = 17


17 correct answers
13 wrong answers

Similar Triangles

Triangle Diagram

Question

The diagram shows a pair of similar triangles, with corresponding angles marked. 

Calculate the values of X & Y.

Answer

ΔABC is similar to ΔDEF

Y/9 = 8/6

So: 

Y=12cm

8/10 = 6/X

X = 7.5cm (Remember Units)

Y = 12cm          X = 7.5cm

Athlete's Problem

Question
An athlete covers 3 consecutive miles by walking the first mile, running the second and cycling the third. He runs twice as fas as he walk, and cycles one and a half times as fast as he runs. He takes 10 minutes longer than he would do if he cycled the three miles.
How long does he take by walking, cycling and running?

Answer

	Distance	Time	Speed
Walk	1	1/X	X (Let ‘x’ be walking speed)
Run	1	1/2X	2X (He runs twice as fast as he runs)
Cycle	1	1/3X	3X ( He cycles one and a half times as fast as he runs)

T = D/S
T = 1+1+1/3X
T = 3/3X


10 minutes = 10/60 = 1/6


1/6 + 3/3X = 1/X + 1/2X + 1/3X (*6X)
X + 6 = 6 + 3 +2
X = 5


So:

• walking = 1/5 
• running = 1/10
• cycling = 1/15

1/5 + 1/10 + 1/15 = 11/30 = 22/60


22 minutes

3 & 4 Legged Tables

Question

Several three-legged tables and four-legged table have a total of 23 legs. If there is more than one table of each type, what is the number of three-legged tables?

A) 6

B) 7

C) 3

D) 4

E)  5

Answer
The simplest way of doing this is by writing out the number of legs in a table (shown below)

Tables	‘3 Legged’ Tables	‘4 Legged’ Tables	To Make 23
1	3	4
2	6	8	15
3	9	12	11 (not a multi. of 3)
4	12	16	7 (not a multi. of 3)
5	15	20
6	18	24
7	21
8	24

As shown above:

• 8 legs are allowed '4 legged table'
• 15 legs are allowed '3 legged table'

So: 5 = 3 'legged table'

       2 = 4 'legged table'   

E = 5

                                                                                                             

The Petrol Problem

Question


The petrol tank in Bob's car is 1/8 full. When 30 litres of petrol are added, the tank become 3/4 full. If the petrol costs $1.38 per litre, how much will it cost her to fill the remaining quater of the tank?


A) $8.80
B) $13.80
C) $16.56
D) $24.84
E) $41.40


Answer & Working


1/8 + 30L = 3/4


3/4  - 1/8
6/8  - 1/8 = 5/8
-------------------------------------- 
Let 'x' be the full fuel tank


5/8x = 30
x = 48L (The full fuel tank can hold 48L)


1/4x = 48/4
1/4x = 12L (So a quarter of the tank contains 12L)


(Now we have to find how much 12L costs)
12 * 1.38


C = $16.56 (Remember the units)