A Math Problem

JoeMoma

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Tom, Sue, Bob & LaTasha went to the mall. Tom spent 100 dollars. Sue spent 4 times less than Tom. Bob spent 2 times less than Tom. LaTasha Spent 1 time less than Tom. How much money did Sue, Bob and LaTasha spend each?
 

Pogo

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Tom, Sue, Bob & LaTasha went to the mall. Tom spent 100 dollars. Sue spent 4 times less than Tom. Bob spent 2 times less than Tom. LaTasha Spent 1 time less than Tom. How much money did Sue, Bob and LaTasha spend each?
25, 50, 0.

Switching the names around, I see what you did there.
 
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JoeMoma

JoeMoma

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Tom, Sue, Bob & LaTasha went to the mall. Tom spent 100 dollars. Sue spent 4 times less than Tom. Bob spent 2 times less than Tom. LaTasha Spent 1 time less than Tom. How much money did Sue, Bob and LaTasha spend each?
25, 50, 0.

Switching the names around, I see what you did there.
Were the names switched around?
 

Pogo

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Tom, Sue, Bob & LaTasha went to the mall. Tom spent 100 dollars. Sue spent 4 times less than Tom. Bob spent 2 times less than Tom. LaTasha Spent 1 time less than Tom. How much money did Sue, Bob and LaTasha spend each?
25, 50, 0.

Switching the names around, I see what you did there.
Were the names switched around?
Oops, sorry I guess not.

Do we have the right answer?
 
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JoeMoma

JoeMoma

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Usually when the phrase "n times less" is used, in which n is the number of times less, the intended interpretation is 1/n times as much.

Using this interpretation the calculations are as follows:

Sue: 1/4 x $100 = $25
Bob: 1/2 x $100 = $50
LaTasha: 1/1 x $100 = $100

The above interpretation does not make sense literally. How can LaTasha spend 1 time less than Tom and still spend exactly the same amount as Tom? Wouldn't $100 be zero times less than what Tom spent? But 1/0 is undefined! Note, several posters used the "1/n times" interpretation for "4 times less" and "2 times less" and used a completely different calculation for "1 time less".

A literal interpretation of "n times less" would mean the original amount minus n times the original amount. Interpreting "n times less" literally, the calculations are as follows:

Sue: $100 - 4 x $100 = - $300
Bob: $100 - 2 x $100 = - $100
LaTasha: $100 - 1 x $100 = $0

Interesting that 2 posters used the "1/n times as much" interpretation for Sue and Bob, but the literal interpretation for LaTasha.
 

Quasar44

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Just break it into algebra expressions
This is 9th grade Algebra
 

Grumblenuts

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The problem is presuming some "correct" answer exists or that some "literal" interpretation applies to begin with. Not so in many contexts. The SA article mentions "weight" of graphene vs steel confusion where tensile strength density is what's actually being compared. Weight being a vastly misused and abused term. Often there's no foolproof rule or procedure. One is just going to be lost until they acclimate. Learning the colloquial is on you. The entire context must often be considered and then from different angles..
 

Pogo

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Usually when the phrase "n times less" is used, in which n is the number of times less, the intended interpretation is 1/n times as much.

Using this interpretation the calculations are as follows:

Sue: 1/4 x $100 = $25
Bob: 1/2 x $100 = $50
LaTasha: 1/1 x $100 = $100

The above interpretation does not make sense literally. How can LaTasha spend 1 time less than Tom and still spend exactly the same amount as Tom? Wouldn't $100 be zero times less than what Tom spent? But 1/0 is undefined! Note, several posters used the "1/n times" interpretation for "4 times less" and "2 times less" and used a completely different calculation for "1 time less".

A literal interpretation of "n times less" would mean the original amount minus n times the original amount. Interpreting "n times less" literally, the calculations are as follows:

Sue: $100 - 4 x $100 = - $300
Bob: $100 - 2 x $100 = - $100
LaTasha: $100 - 1 x $100 = $0

Interesting that 2 posters used the "1/n times as much" interpretation for Sue and Bob, but the literal interpretation for LaTasha.
I don't see the inconsistency and I didn't use fractions.

"4 times less" is N x 0.25. "2 times less" is N x 0.5 and "1 time less", which is not a common phrase in English, I interpreted to mean "equal to" (100 = 100), so subtract 100 from 100, equals zero.
 

Turtlesoup

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Tom, Sue, Bob & LaTasha went to the mall. Tom spent 100 dollars. Sue spent 4 times less than Tom. Bob spent 2 times less than Tom. LaTasha Spent 1 time less than Tom. How much money did Sue, Bob and LaTasha spend each?
Tom $100
Sue $25
Bob $50
Latasha stole everything and really didn't "spend" anything.
 

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