If my age is divided by 3, the remainder is 2. If my age is divided by 5, the remainder is also 2. If my age is divided by 7, the remainder is 5. How old am I?

Question

anonymous · Answer

If my age is divided by 3, the remainder is 2. If my age is divided by 5, the remainder is also 2. If my age is divided by 7, the remainder is 5. How old am I?

xapproachesinfinity · Answer

we could set it this way
a=3b+2
a=5c+2
a=7d+5
a= is your age
b,c,d is what you multiply 3,5,7 to get close to your age with remainder 2,2,5
a-3b=2
a-5c=2
a-7d=5
solve this system
you could have other different ways

xapproachesinfinity · Answer

actually this went get you any way! but it gives us a hint
(a-2) is multiple of 5 and 3

xapproachesinfinity · Answer

common multiples of 5 and 3
{5,10,15,20,25,30.....}
(3,6,9,12,15,18, 21,...}
so least common multiple is 15
but we have another problem here
a-5 is a multiple of 7
{7, 14, 21, 28, 35, 42, 49...}

xapproachesinfinity · Answer

so what we need now is to work multiple of 15 add 2
and multiple of 7 add 5
{17, 32, 47, 62...} for 15
{12, 19, 26, 33, 40. 47, 54...}'
we observe that 47 is common here
so it has to be the solution

anonymous · Answer

thanks

anonymous · Answer

That answer was in the back of my head

xapproachesinfinity · Answer

no checking!
47 divided by 3 we g3t remainder of 2 
47 divided by 5 we get remainder of 2
47 divided by 7 we remainder of 5
so it is indeed 47

xapproachesinfinity · Answer

get*

xapproachesinfinity · Answer

you are welcome^_^

anonymous · Answer

I want to ask you another question Classify all the numbers that leave a remainder of 3 when divided by 5 and a remainder of 1 when divided by 3

xapproachesinfinity · Answer

hmmm x=5a+3
y=3b+1
so x is multiple of 5 add 3
and y is a multiple of 3 add 1
for 3
{5,10,15, 20,25,30...}
{8,13,18, 23,28,33...}
for 3
{3,6,12,15,18,21...}
{4,7,13,16,19,22,25...}

anonymous · Answer

are u surre

xapproachesinfinity · Answer

that's not the answer
we need to see what number have that condition btw all those numbers

anonymous · Answer

ohh

xapproachesinfinity · Answer

{8,13,18, 23,28,33...}
{4,7,13,16,19,22,25...}
you need to see it here

xapproachesinfinity · Answer

it seems that there is only one number 13
that satisfies this conditions
however you need to extend those to braces you might find other numbers that have the same condition, i'm too lazy to continue counting this haha

xapproachesinfinity · Answer

13/5 remainder 3
13/3 remainder 1
you need to see it like this

anonymous · Answer

is there more cause they say its a list

xapproachesinfinity · Answer

could be! i only did few you will have to continue the list of two
and choose the common ones and see if they satisfy the same condition

anonymous · Answer

28 works too

xapproachesinfinity · Answer

yeah! that one too

xapproachesinfinity · Answer

well 28 is common btw the two, if i continued i would get 28 after 25

xapproachesinfinity · Answer

they have to be common
carry the on the rest tell you see some pattern or something
you might get a conclusion

anonymous · Answer

can u try to find a equation

xapproachesinfinity · Answer

hmmm an equation, don't it works that way haha

anonymous · Answer

43 works
and I found the equation and why

xapproachesinfinity · Answer

oh yeah! sounds good! let me see

anonymous · Answer

the numbers that works are 13 + 5 * 3

anonymous · Answer

then 28 + 5*3

anonymous · Answer

can u help me make an equation with variables

xapproachesinfinity · Answer

oh very clever my friend that is the pattern here

anonymous · Answer

thanks I am a human calculator

anonymous · Answer

what grade u in I am going to 8

xapproachesinfinity · Answer

i was too lazy to carry on hehe!

anonymous · Answer

please help me make an equation

xapproachesinfinity · Answer

oh this a sequence my friend the first term being 13 and the common difference of 15
have you studied this!
about my grade, i'm a college student

anonymous · Answer

I did but this sequence can go on forever and I have to make a list

xapproachesinfinity · Answer

well have you studied sequences or not!

anonymous · Answer

i did

xapproachesinfinity · Answer

it doesn't matter if it goes for ever

anonymous · Answer

i am taking the shsat

xapproachesinfinity · Answer

ok now we can proceed! this sequence is what kind of sequences?

xapproachesinfinity · Answer

it is an arithmetic sequence, right?
what do you know about this sequence

xapproachesinfinity · Answer

what is the general term

anonymous · Answer

it has a rate

xapproachesinfinity · Answer

not rate, we call it common different
the general term is like this 
An=A1+(n-1)d
A1 first term
d common difference

xapproachesinfinity · Answer

do you remember this?

anonymous · Answer

yeah

anonymous · Answer

so the A1 is 13 and the comman difference is 15, right

xapproachesinfinity · Answer

yeah!
so An=13+15(n-1)
then we can say that the numbers that satisfy this equation are the numbers that
satisfies the condition for any n>=1

xapproachesinfinity · Answer

actually we have the say that the term that that equation generates
are the numbers that satisfy the condition for any n>=0
======
my sentence above is incorrect!

xapproachesinfinity · Answer

actually we have to say that the terms that that equation generates
are the numbers that satisfy the condition for any n>=0

xapproachesinfinity · Answer

sorry for bad spelling hehe

anonymous · Answer

so are we finished

xapproachesinfinity · Answer

yeah! that's all you need!

xapproachesinfinity · Answer

you don't have to make a list

anonymous · Answer

bye I will get your help next time

xapproachesinfinity · Answer

alright! perhaps i get of help to you!
just tag me, and we'll see^_^

anonymous · Answer

ok

xapproachesinfinity · Answer

8 grade is high school?
i don't understand the system here that much

anonymous · Answer

I am in middle school

xapproachesinfinity · Answer

i see, good luck^_^
study hard!