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

Question

asked Sep 3, 2024 152k views

1 Answer

McMath · Answer 1 · 2024-09-08T14:19:29+0000

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.