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

  • Context: High School 
  • Thread starter Thread starter JasonRox
  • Start date Start date
  • Tags Tags
    Short
Click For Summary

Discussion Overview

The discussion revolves around a mathematical problem involving the relationship between two numbers, where participants are tasked with finding the numbers based on given conditions. The scope includes problem-solving and mathematical reasoning.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a problem stating that the larger number exceeds twice the smaller by 1, and three times the smaller is 6 more than the larger.
  • Another participant claims to have found the numbers as 7 and 15, suggesting a playful tone about receiving a reward for their solution.
  • A different participant presents the numbers as 15 and 7, asking for recognition of their answer.
  • One participant provides a breakdown of the equations derived from the problem, showing the steps to arrive at the solution of 15 and 7, while emphasizing the importance of checking the original problem statement.
  • There is a critique regarding the use of different variable names (m, n, A, B) instead of the original context, suggesting that this could lead to a loss of points in a formal setting.

Areas of Agreement / Disagreement

Participants generally agree on the solution being 15 and 7, but there is contention regarding the proper representation of the variables used in the problem. Some participants challenge the naming conventions used by others.

Contextual Notes

The discussion does not resolve the issue of variable naming and its implications for answering the problem correctly. There is also an emphasis on the importance of checking the original wording of the problem against the derived equations.

JasonRox
Homework Helper
Gold Member
Messages
2,394
Reaction score
4
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. :biggrin:
 
Mathematics news on Phys.org
n = 7 and m = 15.

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

cookiemonster
 
A = 15 and B = 7. What do I get?
 
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.
 
HallsofIvy said:
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. :wink:
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 24 ·
Replies
24
Views
7K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 11 ·
Replies
11
Views
7K
  • · Replies 11 ·
Replies
11
Views
7K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K