Math Is Fun Forum

#7
The ratio of annual incomes of two persons is 9:7 and the ratio of their annual expenditure is 4:3. Each of them saves $2000 yearly. Find their annual incomes.

31,100 = S - [500+0.04(s-10,000)]
31,100 = S -[500 + 0.04s - 400]
31,100 = S - 100 - 0.04s
31,200 = 0.96 S
S = 31,200 / 0.96
S = 32,500

Problem #6

A salesman's commission is 5% on all sales up to $10,000 and 4% on all sales exceeding this. He remits $31,100 to his parent company after deducting his commission. His sales was worth $_________.

Reminded me of an old joke:-

The European Union commissioners have announced that agreement has been reached to adopt English as the preferred language for European communications, rather than German, which was the other possibility.

As part of the negotiations, Her Majesty's Government conceded that English spelling had some room for improvement and has accepted a five-year phased plan for what will be known as EuroEnglish (Euro for short).

In the first year, 's' will be used instead of the soft 'c'. Sertainly, sivil servants will resieve this news with joy. Also, the hard 'c' will be replaced with 'k.' Not only will this klear up konfusion, but typewriters kan have one less letter.

There will be growing publik enthusiasm in the sekond year, when the troublesome 'ph' will be replaced by 'f'. This will make words like 'fotograf' 20 per sent shorter.

In the third year, publik akseptanse of the new spelling kan be expekted to reach the stage where more komplikated changes are possible. Governments will enkourage the removal of double letters, which have always ben a deterent to akurate speling. Also, al wil agre that the horible mes of silent 'e's in the languag is disgrasful, and they would go.

By the fourth year, peopl wil be reseptiv to steps such as replasing 'th' by 'z' and 'w' by 'v'.

During ze fifz year, ze unesesary 'o' kan be dropd from vords kontaining 'ou', and similar changes vud of kors; be aplid to ozer kombinations of leters.

After zis fifz yer, ve vil hav a reli sensibl riten styl. Zer vil b no mor trubls or difikultis and evrivun vil find it ezi tu understand ech ozer. Ze drem vil finali kum tru.

You got it √

A person was born in 1975 and he died in 1995. He was 25 years of age when he died. How?

(This one's a lateral thinking puzzle )

I once knew someone named justlooking,
Who had a knack for hookin'
Everytime he tried his skill

Ist truck:-    3 full cylinders, 1 half-full and 3 empty
IInd truck:-  2 full cylinders, 3 half-full and 2 empty
IIIrd truck:- 2 full cylinders, 3 half-full and 2 empty

PS:- The Moderator may remove my reply if he/she wants it to be left open.

Jenilia, we shall prepare you for the Olympiad;
I shall start with my first lesson,
do you know how recurring decimals are converted into fractions?
Lets assume x=0.1414141414....................
100 x = 14.14141414.....................
Deducting equation (2) from (1),
99x = 14
x = 14/99

I saw this problem and I was impressed. I didn't know someone had posted a similiar problem earlier. Okay, I shall give the solution and post a new problem instead.
The solution :- 6 /(1-3/4)

The new problem #3
Imagine you are writing numbers from 1 to 1000 on a piece of paper. How many times would you write the number'9'?

I shall try to solve that when I start the next week,
here's my problem for the day

Using the numbers 1, 3, 4, and 6, together with the operations +, -, ×, and ÷, and unlimited use of brackets, make the number 24.  Each number must be used precisely once.  Each operation may be used zero or more times.  Decimal points are not allowed, nor is implicit use of base 10 by concatenating digits, as in 64 - 31.

I am jumping in!