TINAGARAN A/L MAGIS PARAN

(901117-04-5295)

MUHAMMAD BIN RAZALI

(900629-03-5213)

NON-ROUTINE PROBLEM

QUESTION 4

As he grew older, Abraham De Moivre (1667-

1754), a mathematician who helped in the

development of probability, discovered one

day that he had begun to require 15 minutes

more sleep each day. Based on the

assumption that he required 8 hours of sleep

on date A and that from date A he had begun

to require an additonal 15 minutes of sleep

each day, he predicted when he would die.

The predicted date of death was the day

when he would require 24 hours of sleep. If

this indeed happened, how many days did he

live from date A?

STRATEGY

Write an Equation

STEP 1

UNDERSTAND THE PROBLEM De Moivre found that if he needed 8 hours

of sleep on Monday, for example, then he

needed 8 hours and 15 minutes of sleep

on Tuesday, 8 hours and 30 minutes on

Wednesday.

If we assume his prediction to be correct,

we are to determine how many days he

live until he required 24 hours of sleep.

The only other needed information is that

there are 60 minutes in an hour.

STEP 2

DEVISING A PLAN Use the strategy to write an equation

We recognize that the problem entails

looking at an arithmetic sequence

The difference in this case is 15

minutes, or 16/60 or ¼ of an hour.

The 1st term in the sequence is 8 + 1/4

, and we need to know the number of the

term which has value 24.

STEP 3

CARRYING OUT THE PLAN

Number of term Term

1

2

3

.

.

.

n

8 + ¼

8 + ¼ + ¼ = 8 + 2( ¼)

8 + ¼ + ¼ + ¼ = 8 + 3( ¼)

.

.

.

8 + n(1/4) = 24

Hence, we need to do is solve the equation :

24 = 8 + n(1/4)

24 = 8 + n(1/4)

we see that 8 plus some number is 24

16 = n(1/4)

that number must be 16

4(16) = n

64 = n

Answer : De Moivre can live 64 days

STEP 4

LOOKING BACK

Using the strategy of write an equation,

we found that De Moivre can live 64 days

after date A