SOLUTION: the sum of the last two digits of a three digit counting number is 7. the sum of the first two digits is 5. the middle digit is 4 times the first digit. what is the number?

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Question 134137: the sum of the last two digits of a three digit counting number is 7. the sum of the first two digits is 5. the middle digit is 4 times the first digit. what is the number?
Found 2 solutions by solver91311, oscargut:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Three digit number, so the digits are h for hundreds, t for tens, and o for ones.

The sum of the last two digits is 7: t+%2B+o+=+7
The sum of the first two digits is 5: h+%2B+t+=+5
The middle digit is 4 times the first digit: t=4h

We can substitute t=4h for t in h+%2B+t+=+5 giving us h%2B4h=5, and solve for h: 5h=5 => h=1

Knowing that h=1 we can use h%2Bt=5 to determine that t=4.

Knowing that t=4 we can use t%2Bo=7 to determine that o=3.

Therefore the number is 143.
4 + 3 = 7
4 + 1 = 5, and
4 = 4(1)
Answer checks.




Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
let the digits x,y and z
then
y+z=7 (1st eq)
x+y=5 (2nd eq)
y=4x (3rd eq)
then using y = 4x and 2nd eq
5x=5
then x=1, y=4 and z=7-y=3
Answer: number is 143