SOLUTION: it is a 4 digit number. the 2 digit is two times greater than the 3. the sum of all digits is three times than the last digit of the number. the product of the 3 and 4 digit is 12
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Question 507472: it is a 4 digit number. the 2 digit is two times greater than the 3. the sum of all digits is three times than the last digit of the number. the product of the 3 and 4 digit is 12 times bigger than the ratio of the 2 to 3.? Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Write an equation for each statement, simplify and substitute if possible:
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It is a 4 digit number.
a, b, c, d; are the digits
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The 2nd digit is two times greater than the 3rd.
b = 2c
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the sum of all digits is three times than the last digit of the number.
a + b + c + d = 3d
a + b + c = 3d - d
a + b + c = 2d
substitute 2c for b
a + 2c + c = 2d
a + 3c = 2d
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the product of the 3 and 4 digit is 12 times bigger than the ratio of the 2nd to 3rd.?
c*d = 12()
Replace b with 2c
c*d = 12()
Cancel c and we have
c*d = 24
We have 4 unknowns and 3 equations, so we will have to make an logical guess
c=3, d=8; seems logical (d has to be the larger factor)
Go with that and using the 2nd equation we have:
a + 3c = 2d
a + 3(3) = 2(8)
a + 9 = 16
a = 16 - 9
a = 7
and
b = 2(3)
b = 6
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Our number: 7638
;
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Check this using a + b + c + d = 3d
7 + 6 + 3 + 8 = 3(8)
24 = 24
