Maths

[Igcse100]

Please help me with this question

Luis and Hans both have their birthdays on January 1st.
In 2002 Luis is 13 and Hans is 17 years old.
(a) Which is the next year after 2002 when both their ages will be prime numbers?
Answer (a) ......................................................
(b) In which year was Hans twice as old as Luis?
Answer (b) ......................................................

 

[XPFMember]

for a part just find out a prime no. such that the successive prime numbers differ by 4 since the difference between their ages is 4!!so after 13 the list of prime numbers goes like this.....13,17,19,23,29...now if u see 19 and 23 have a difference of 4!! so then find out the year when luis is 19 and hans is 23 ...u get it as 2008(luis will become 19 after 6 years so 2002+6 = 2008)
Ans. : 2008


for b part u can make two equations!Lets suppose that age of luis is x and hans is y....since we know the difference between hans and luis will always be 4 we can write an equation-----> y - x = 4
now we have two find the x and y values when (their ages) when y (Hans's age) is twice as x(luis's age)
so another equation ----->y= 2x

solve the two equations simultaneously
the solutions will be : x = 4 and y = 8
since u need to find the year find out in which year was hans 8 years old.....it's 1993!!
Hope u understood...any thing still nt clear ..let me know!

 

[Igcse100]

May God bless thank u very much tk

 

[XPFMember]

no problem...i saw ur chemistry questions...will soon answer it!!!