the sum of 2 numbers is 249. twice the larger plus 3 times the smaller is 591. find the numbers. show your work.

Question

the sum of 2 numbers is 249. twice the larger plus 3 times the smaller is 591. find the numbers. show your work.

Answer 1

Let x and y be the two numbers.  Let y be the larger number.

 

x + y = 249

 

3x + 2y = 591

 

Now solve this system of 2 equations in 2 unknowns.

 

From the top equation get

 

x = 249 - y

 

and substitute for x in the bottom equation to find y:

 

3(249 - y) + 2y = 591

 

747 - 3y + 2y = 591

 

-y = -156

 

y = 156

 

Then x = 249 - y = 249 - 156 = 93

 

The two numbers are 93 and 156.