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The sum of two numbers is 209. If one number is 7 less than two times of the other, then find the two numbers​

User Ron Whites
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Let's assume the first number is represented by "x" and the second number is represented by "y."

According to the given information, we have two equations:

1) The sum of the two numbers is 209:


\displaystyle\sf x+y=209

2) One number is 7 less than two times the other:


\displaystyle\sf x=2y-7

To solve this system of equations, we can use substitution or elimination.

Substitution method:

We substitute the value of x from the second equation into the first equation:


\displaystyle\sf (2y-7)+y=209

Simplifying the equation:


\displaystyle\sf 3y-7=209

Adding 7 to both sides:


\displaystyle\sf 3y=216

Dividing both sides by 3:


\displaystyle\sf y=72

Now, substitute the value of y back into the second equation to find x:


\displaystyle\sf x=2(72)-7


\displaystyle\sf x=137

So the two numbers are x = 137 and y = 72.

User McMath
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