Find the larger number

Question

One number is 1 less than a second number. Twice the second number is 40 less than 5 times the first. Find the larger number

Answer 1

Hi Nicole,

 

This problem can be solved using systems of equations.  While there are 2 or 3 ways to solve, I think the substitution method would be best.  Let's start with the 2 equations based on the information given.  Let's us x for the 1st number, and y for the 2nd (which is the larger).

 

   x = y -1 (one number is 1 less than a second number)

   2y = 5x - 40  (twice the 2nd # is 40 less than 5 times the 1st)

 

Now we'll substitute y-1 for x in the second equation, because we know they're equal.

 

   2y = 5(y-1) - 40

 

I expect you can take it from here.  In case you need help ...

 

   2y = 5y - 5 - 40 ...  2y = 5y - 45  ...  -3y = -45  ...  y = 15

 

It's always good to double check your results.  Also, although it's easy to figure out what x (the smaller number) is, the question is asking for the larger number.

 

Paul L.