Height of Each Brother

[nycmathguy]

Next door to me live four brothers of different heights. Their average height is 74 inches, and the difference in height among the first three men is two inches. The difference between the third and fourth men is six inches. Can you tell how tall is each brother?

Let me see.

There are 4 brothers.
Each brother is about 74 inches tall.

Let x = age of each brother.

Here's where I got lost:

". . .the difference in height among the first three men is two inches. The difference between the third and fourth men is six inches."

How is the quote above translated into algebra?

Stuck....

 

[MathLover1]

Let 1st be a, 2nd be b, 3rd be c & 4th be d

given that the difference in height among the first three men is 2 inches, so

a = a
b = a+2
c = b+2 = a+2+2=a+4
The difference between the third and fourth men is 6 inches
d = c+6 = a+4+6=a+10

Thus, the average is
74=(a +b +c +d)/4...............substitute b, c, and d

74=(a+a+2+a+4+a+10)/4

74=(4a+16)/4

74=a+4

a=70

Thus,

b = a+2 = 70+2 = 72

c = a+4 = 70+4 = 74

d = a+10 = 70+10 = 80

the height of 4 brothers are as follow:

1st - 70 Inches

2nd - 72 inches

3rd - 74 inches

4th - 80 inches

 

[nycmathguy]

Let 1st be a, 2nd be b, 3rd be c & 4th be d

given that the difference in height among the first three men is 2 inches, so

a = a
b = a+2
c = b+2 = a+2+2=a+4
The difference between the third and fourth men is 6 inches
d = c+6 = a+4+6=a+10

Thus, the average is
74=(a +b +c +d)/4...............substitute b, c, and d

74=(a+a+2+a+4+a+10)/4

74=(4a+16)/4

74=a+4

a=70

Thus,

b = a+2 = 70+2 = 72

c = a+4 = 70+4 = 74

d = a+10 = 70+10 = 80

the height of 4 brothers are as follow:

1st - 70 Inches

2nd - 72 inches

3rd - 74 inches

4th - 80 inches

I give up. I could never reason my way through the problem as you did. Feeling frustrated. Ha!

 

[Country Boy]

I would say that "the difference in height among the first three men is two inches" is ambiguous. It could mean that B is two inches taller than A and C is two inches taller than B (so four inches taller than A) of it could mean that the tallest of the the three men is two inches taller than the shortest with the third somewhere in between.

Of course, in order to be able to solve this problem you have to assume the first as you did so I am just nit-picking.

 

[nycmathguy]

I would say that "the difference in height among the first three men is two inches" is ambiguous. It could mean that B is two inches taller than A and C is two inches taller than B (so four inches taller than A) of it could mean that the tallest of the the three men is two inches taller than the shortest with the third somewhere in between.

Of course, in order to be able to solve this problem you have to assume the first as you did so I am just nit-picking.

If the question is unclear to you, think how totally unclear it is to me.

 

[Country Boy]

If the question is unclear to you, think how totally unclear it is to me.

I did not say it was "unclear", I said it was "ambiguous". Those are not the same!

 

[nycmathguy]

I did not say it was "unclear", I said it was "ambiguous". Those are not the same!

Ambiguous or whatever the word, the problem is unclear to me.

 

[MathLover1]

Ambiguous or whatever the word, the problem is unclear to me.

am·big·u·ous
/amˈbiɡyo͞oəs/
Learn to pronounce

adjective

1. (of language) open to more than one interpretation; having a double meaning.
   "ambiguous phrases"
   • unclear or inexact because a choice between alternatives has not been made.
     "the election result was ambiguous"

practically same

 

[nycmathguy]

am·big·u·ous
/amˈbiɡyo͞oəs/
Learn to pronounce

adjective

1. (of language) open to more than one interpretation; having a double meaning.
   "ambiguous phrases"
   • unclear or inexact because a choice between alternatives has not been made.
     "the election result was ambiguous"

practically same

Exactly. Almost the same in meaning. By the way, I have put aside math during the week. Dealing with a lot of stuff back home, as you could well imagine.

A. My roommate has become abusive. Not helping me with bills, stealing my food, using my toilet paper, bounty paper towels, etc.

B. Still no heat in my room in the middle of winter. The house owner has been putting aside calling a professional heating company to fix the problem. The radiator is broken.

Sorry. . .this is a math forum.

 

[MathLover1]

if he house owner has been putting aside calling a professional heating company to fix the problem, you have right to move somewhere else

 

[nycmathguy]

if he house owner has been putting aside calling a professional heating company to fix the problem, you have right to move somewhere else

I am looking for a room as I type this to you.