SOLUTION: A 2 digit number is 3 more than 7 times the sum of its digits. If the digits are interchange, the new number is 4 more than 5 times the tens digit of the original number.What's the

Algebra ->  Equations -> SOLUTION: A 2 digit number is 3 more than 7 times the sum of its digits. If the digits are interchange, the new number is 4 more than 5 times the tens digit of the original number.What's the      Log On


   

Question 92688: A 2 digit number is 3 more than 7 times the sum of its digits. If the digits are interchange, the new number is 4 more than 5 times the tens digit of the original number.What's the original number?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A 2 digit number is 3 more than 7 times the sum of its digits. If the digits are interchange, the new number is 4 more than 5 times the tens digit of the original number.What's the original number?
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10's digit = x; Units digit = y:
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Write the equation for:
"A 2 digit number is 3 more than 7 times the sum of its digits."
10x + y = 7(x+y) + 3
Simplify
10x + y = 7x + 7y + 3
10x - 7x + y - 7y = 3
3x - 6y = 3
3x = 6y + 3
x = 2y + 1; divided equation by 3
:
"If the digits are interchange, the new number is 4 more than 5 times the tens digit of the original number."
10y + x = 5x + 4
10y - 5x + x = 4
10y - 4x = 4
Substitute (2y+1) for x, find y
10y - 4(2y+1) = 4
10y - 8y - 4 = 4
2y = 4 + 4
2y = 8
y = 4
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Find x using x - 2y + 1
x = 2(4) + 1
x = 8 + 1
x = 9
:
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Original two digit number = 94
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Check our solutions in the two statement equations