Find the Two Numbers: A Tricky Math Problem Solved in 5 Minutes

[JasonRox]

I usually get them, but this one got me stuck.

Here it is:

The larger of two numbers exceeds twice the smaller number by 1. Three times the smaller number is 6 more than the larger. Find the two numbers.

Well I got it just after I finish writing it. A 5 minute break usually does it.

Take a shot at it.

I'll post the answers later or congragulate the lucky/smart person.

 

[cookiemonster]

n = 7 and m = 15.

Do I get a cookie for paying attention in algebra class?

cookiemonster

 

[Chen]

A = 15 and B = 7. What do I get?

 

[HallsofIvy]

Let "x" represent the larger number, "y" the smaller.

"The larger of two numbers exceeds twice the smaller number by 1."
x= 2y+ 1

" Three times the smaller number is 6 more than the larger. "
3y= x+ 6

Since x= 2y+1, the second equation becomes 3y= 2y+1+ 6 or y= 7. Then
x= 2(7)+ 1= 15.

Check: 15 exceeds twice 7 by 1 and 3 times 7 (21) is 6 more than 15.
(It's always best to check by going back to the original words- not the equations you got from the words- you might have done that wrong!)

And the most important point- write the answer clearly:

The larger of the two numbers is 15 and the other number is 7.

Chen and Cookiemonster: A really sharp teacher would take a point off: the problem said nothing about "m and n" or "A and B" and so you did not in fact answer the problem.

 

[Chen]

Chen and Cookiemonster: A really sharp teacher would take a point off: the problem said nothing about "m and n" or "A and B" and so you did not in fact answer the problem.

A really sharp teacher would never ask this question, so we are safe.