sum of two numbers

Question

The sum of two numbers is
123. 
If
three times
the smaller number is subtracted from the larger? number, the result is
11  
Find the two numbers.

Answer 1

Jessica,

 

Let 'x' be the smaller of the two and 'y' be the larger.

 

Now first, we know that the sum of the two equals 123:

 

x + y = 123

 

Second, we know that the larger number minus 3 times the smaller equals 11:

 

y - 3x = 11

 

Rewrite this eq to isolate y:

 

y = 3x + 11

 

Now, substitute this value of y for y in the first equation (x + y = 123):

 

x + 3x + 11 = 123

 

Combine like terms:

 

4x + 11 = 123

 

Subtract 11 from both sides:

 

4x = 112

 

Divide both sides by 4:

 

4x/4 = 112/4

 

x = 28

 

Now, since x + y = 123:

 

28 + y = 123 => y = 123 - 28 = 95

 

Hope this helps!

Answer 2

Hi Jessica,

We know:

x+y=123 and y-3x=11

 

We can rearrange one of the equations and solve for one variable (let's take the first equation and solve for y):

y=123-x

 

Now we can substitute 123-x in for y in the other equation:

(123-x)-3x=11

 

Solve for x, then plug back into the rearranged first equation to solve for y.