SOLUTION: one number is 7 less than the second number. twice the second number is 7 less than 5 times the first. find the smaller of the two.

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Question 707091: one number is 7 less than the second number. twice the second number is 7 less than 5 times the first. find the smaller of the two.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
a is first number; b is second number.

one number is 7 less than the second number. a=-7%2Bb
twice the second number is 7 less than 5 times the first. 2b=-7%2B5a
find the smaller of the two.

Those two equations turn into system:
a-b=-7
5a-2b=7

Multiply first equation by 2 and subtract from the second equation.
2a-2b=-14
5a-2b=7

5a-2b-(2a-2b)=7-(-14)
3a+0=+7
a=7%2F3, same as a=2%261%2F3

Use a to find b. Using original first equation, a=-7+b, b=a+7,
b=7/3+7=9%261%2F3=b