SOLUTION: The sum of two numbers is 70. The second is 1 more than 2 times the first. What are the two numbers?

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Question 102599: The sum of two numbers is 70. The second is 1 more than 2 times the first. What are the two numbers?
Answer by mjgulinello(10) About Me  (Show Source):
You can put this solution on YOUR website!
Let M = the first number.
Let N = the second number.
We know the sum is 70, so
M+%2B+N+=+70
We also know the second number is 1 more than 2 times the first number, which we can express as
N+=+2M+%2B+1
Now use substitution and plug the second equation into the first.
M+%2B+%282M+%2B1%29+=+70
Combine like terms
3M+%2B+1++=+70
Subtract 1 from each side
3M+=+69
Divide each side by 3
M+=+23
Now we can plus this into the second equation.
N+=+2M+%2B+1
N+=+2+%2A+23+%2B+1
N+=+46+%2B+1
N=47
The two numbers are 23 and 47.
We can check this by plugging the numbers back into the first equation.
M+%2B+N+=+70
23+%2B+47+=+70
70=70
Check.
That's all for this problem.