Mwanafunzi, weka swali linalokusumbua ili walimu na wazoefu wakusaidie

Where are the mathematicians? Here is a brain teaser: Quantitative Reasoning.

A house wife forgot her bank account *PIN CODE* which is five digits number, but luckily she remembered some hints on how to recall this *PIN*.
Here are some of the clues
1) The *1st* digit is a square of the *2nd*
2) The sum of the *2nd* and *3rd* is 10
3) The *4th* is equal to the *2nd* plus *1*
4) The *3rd* and the *5th* makes *14*
5) The sum of all the digits is *30*

What is the *PIN CODE*?
 
let 1st digit=a
2nd=b
3rd=c
4th=d
5th=e
1.a=(b)2
2.b+c=10
3.d=b+1
4.e+c=14
5.a+b+c+d+e=30
=> (b)2+b+c+d+e=30 (a=(b)2)
=> (b)2+b+(10-b)+d+e=30 (b+c=10=>c=10-b)
=> (b)2+b+(10-b)+(b+1)+e=30 (d=b+1)
=> (b)2+b+(10-b)+(b+1)+(14-(10-b)=30(e+c=14=>e=14-c=>14-(10-b))
=> (b)2+b+10-b+b+1+14-10+b=30
=> (b)2+2b+15=30
=> (b)2+2b=30-15
=> (b)2+2b-15=0
=> (b)2+5b-3b-15=0
=> b(b+5)-3(b+5)+=0
=> (b+5) (b-3)=0
=> b+5=0 b-3=0
=> b= -5 b= 3
Value ya b itakuwa 3 kwa sababu kwenye pin yoyote hakuna negative digit
b = 3
Kwa ku-substitute equation za hapo juu tunapata

1st digit=9
2nd=3
3rd=7
4th=4
5th=7
Mkuu zawadi yangu please
 
let 1st digit=a
2nd=b
3rd=c
4th=d
5th=e
1.a=(b)2
2.b+c=10
3.d=b+1
4.e+c=14
5.a+b+c+d+e=30
=> (b)2+b+c+d+e=30 (a=(b)2)
=> (b)2+b+(10-b)+d+e=30 (b+c=10=>c=10-b)
=> (b)2+b+(10-b)+(b+1)+e=30 (d=b+1)
=> (b)2+b+(10-b)+(b+1)+(14-(10-b)=30(e+c=14=>e=14-c=>14-(10-b))
=> (b)2+b+10-b+b+1+14-10+b=30
=> (b)2+2b+15=30
=> (b)2+2b=30-15
=> (b)2+2b-15=0
=> (b)2+5b-3b-15=0
=> b(b+5)-3(b+5)+=0
=> (b+5) (b-3)=0
=> b+5=0 b-3=0
=> b= -5 b= 3
Value ya b itakuwa 3 kwa sababu kwenye pin yoyote hakuna negative digit
b = 3
Kwa ku-substitute equation za hapo juu tunapata

1st digit=9
2nd=3
3rd=7
4th=4
5th=7
Mkuu zawadi yangu please
uko vizuri mkuu, hongera!
 
let 1st digit=a
2nd=b
3rd=c
4th=d
5th=e
1.a=(b)2
2.b+c=10
3.d=b+1
4.e+c=14
5.a+b+c+d+e=30
=> (b)2+b+c+d+e=30 (a=(b)2)
=> (b)2+b+(10-b)+d+e=30 (b+c=10=>c=10-b)
=> (b)2+b+(10-b)+(b+1)+e=30 (d=b+1)
=> (b)2+b+(10-b)+(b+1)+(14-(10-b)=30(e+c=14=>e=14-c=>14-(10-b))
=> (b)2+b+10-b+b+1+14-10+b=30
=> (b)2+2b+15=30
=> (b)2+2b=30-15
=> (b)2+2b-15=0
=> (b)2+5b-3b-15=0
=> b(b+5)-3(b+5)+=0
=> (b+5) (b-3)=0
=> b+5=0 b-3=0
=> b= -5 b= 3
Value ya b itakuwa 3 kwa sababu kwenye pin yoyote hakuna negative digit
b = 3
Kwa ku-substitute equation za hapo juu tunapata

1st digit=9
2nd=3
3rd=7
4th=4
5th=7
Mkuu zawadi yangu please

Daaaah, mkuu ni-DM namba yako ya simu
 
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