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1

$begingroup$

I have the following question:

A baker filled a measuring cup with $3/4$ cup of water. He poured $1/2$ of the water into the batter, and then spilled $1/8$ of the water on the floor.

How much water will the baker need to add to what is left in the cup to have 50% more than what he started with?

Now, these are the possible answers given by the question:

• $1/8$ cup.


• $3/8$ cup.


• $1/4$ cup.


• $1/2$ cup.


• $7/8$ cup.

Here's what I did:

We start with $$3/4 rightarrow 6/8,$$ after pouring the water into the batter $$6/8 - 1/2 implies 6/8 - 4/8 = 2/8$$ and after spilling the water $$2/8 - 1/8 = 1/8.$$

Now, to find how much we need to add, we add $50%$ of $3/4$ to the original $3/4$, that is $$(1/2)(3/4) + 3/4 = 3/8 + 6/8 = 9/8.$$

So the total amount of water we need to add is $$9/8 - 1/8 = 8/8.$$ But as you can see this is not one of the possible options.

I don't know if I'm doing something wrong or if the answers are incorrect, I suspect that I'm reading something wrong and there's something I'm just not seeing. I ask for your help with this. Thanks in advance.

arithmetic

share|cite|improve this question

asked Jun 7 '16 at 1:36

Iván GIván G

83

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It doesn't say that he pours $frac{1}{2}$ of a cup, it says he pours half of what he has which is not necessarily a cup. Try working with multiplications instead. $frac{6}{8}-frac{4}{8}$ represents starting with three quarters of a cup of water and then pouring two quarters of a cup of water, not pouring half of what he has.
  $endgroup$
  – JMoravitz
  Jun 7 '16 at 1:38
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Did he spill $frac{1}{8}$ of the water he had left, or $frac{1}{8}$ of the original amount of water he had?
  $endgroup$
  – Mike Pierce
  Jun 7 '16 at 1:44
  
  
  

  
  
  
  

add a comment | 

1

$begingroup$

I have the following question:

A baker filled a measuring cup with $3/4$ cup of water. He poured $1/2$ of the water into the batter, and then spilled $1/8$ of the water on the floor.

How much water will the baker need to add to what is left in the cup to have 50% more than what he started with?

Now, these are the possible answers given by the question:

• $1/8$ cup.


• $3/8$ cup.


• $1/4$ cup.


• $1/2$ cup.


• $7/8$ cup.

Here's what I did:

We start with $$3/4 rightarrow 6/8,$$ after pouring the water into the batter $$6/8 - 1/2 implies 6/8 - 4/8 = 2/8$$ and after spilling the water $$2/8 - 1/8 = 1/8.$$

Now, to find how much we need to add, we add $50%$ of $3/4$ to the original $3/4$, that is $$(1/2)(3/4) + 3/4 = 3/8 + 6/8 = 9/8.$$

So the total amount of water we need to add is $$9/8 - 1/8 = 8/8.$$ But as you can see this is not one of the possible options.

I don't know if I'm doing something wrong or if the answers are incorrect, I suspect that I'm reading something wrong and there's something I'm just not seeing. I ask for your help with this. Thanks in advance.

arithmetic

share|cite|improve this question

asked Jun 7 '16 at 1:36

Iván GIván G

83

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It doesn't say that he pours $frac{1}{2}$ of a cup, it says he pours half of what he has which is not necessarily a cup. Try working with multiplications instead. $frac{6}{8}-frac{4}{8}$ represents starting with three quarters of a cup of water and then pouring two quarters of a cup of water, not pouring half of what he has.
  $endgroup$
  – JMoravitz
  Jun 7 '16 at 1:38
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Did he spill $frac{1}{8}$ of the water he had left, or $frac{1}{8}$ of the original amount of water he had?
  $endgroup$
  – Mike Pierce
  Jun 7 '16 at 1:44
  
  
  

  
  
  
  

add a comment | 

$begingroup$

I have the following question:

A baker filled a measuring cup with $3/4$ cup of water. He poured $1/2$ of the water into the batter, and then spilled $1/8$ of the water on the floor.

How much water will the baker need to add to what is left in the cup to have 50% more than what he started with?

Now, these are the possible answers given by the question:

• $1/8$ cup.


• $3/8$ cup.


• $1/4$ cup.


• $1/2$ cup.


• $7/8$ cup.

Here's what I did:

We start with $$3/4 rightarrow 6/8,$$ after pouring the water into the batter $$6/8 - 1/2 implies 6/8 - 4/8 = 2/8$$ and after spilling the water $$2/8 - 1/8 = 1/8.$$

Now, to find how much we need to add, we add $50%$ of $3/4$ to the original $3/4$, that is $$(1/2)(3/4) + 3/4 = 3/8 + 6/8 = 9/8.$$

So the total amount of water we need to add is $$9/8 - 1/8 = 8/8.$$ But as you can see this is not one of the possible options.

I don't know if I'm doing something wrong or if the answers are incorrect, I suspect that I'm reading something wrong and there's something I'm just not seeing. I ask for your help with this. Thanks in advance.

arithmetic

share|cite|improve this question

asked Jun 7 '16 at 1:36

Iván GIván G

83

$endgroup$

share|cite|improve this question

asked Jun 7 '16 at 1:36

Iván GIván G

83

share|cite|improve this question

asked Jun 7 '16 at 1:36

Iván GIván G

83

asked Jun 7 '16 at 1:36

Iván GIván G

83

asked Jun 7 '16 at 1:36

Iván GIván G

83

3 Answers
3

active

oldest

votes

0

$begingroup$

You may be reading the question wrong. Try to solve it again using a different wording, so instead of subtracting $frac{1}{2}$ cup of the water try subtracting half of the total amount of water, and try the same with the 1/8.

share|cite|improve this answer

answered Jun 7 '16 at 1:50

Discrete MathDiscrete Math

1139

$endgroup$

add a comment | 

2

$begingroup$

Briefly: this question, as presented, is poorly worded.

Less Briefly: you subtracted $frac12$, but you should have multiplied by $1-frac12$ (that is, by $frac12$).

In Detail: the baker poured half "of the water". In ordinary English, we would mean that to mean 'half of the water he had in the measuring cup', not '$frac12$ a cup of water'. If you proceed from here you get the answer $frac78$, which is presumably what was intended.

However, the question then goes on to say that he spilled $frac18$ "of the water" on the floor. Following the logic from before, we would expect this to mean 'an eighth of the water he had in the measuring cup', although this phrase is now itself ambiguous (since it could he 'an eighth of the original amount' or 'an eighth after pouring half'). Neither interpretation gets you an answer on the list, unfortunately.

share|cite|improve this answer

answered Jun 7 '16 at 1:45

Eric StuckyEric Stucky

10.3k32561

$endgroup$

add a comment | 

-1

$begingroup$

I did it like this simply. ( agree wording can be a pain for some)

1.) started with 3/4 and he puts half into batter leaving him with 1/2 of 3/4 = 3/8

2.) he spilled 1/8 on the floor so left with 3/8-1/8 = 2/8 { keep it in this form}

3.) 50% more than he had (3/4) = i do itthis way since we know half of 3/4= 3/8 from above add it to 3/4 = so 3/4 + 3/8 = 9/8

4.) so to get to 9/8 from what he has left 2/8 we need to add back 7/8

share|cite|improve this answer

answered Mar 13 at 3:55

Dizzle DazzleDizzle Dazzle

1

$endgroup$

add a comment | 

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0

$begingroup$

You may be reading the question wrong. Try to solve it again using a different wording, so instead of subtracting $frac{1}{2}$ cup of the water try subtracting half of the total amount of water, and try the same with the 1/8.

share|cite|improve this answer

answered Jun 7 '16 at 1:50

Discrete MathDiscrete Math

1139

$endgroup$

add a comment | 

0

$begingroup$

You may be reading the question wrong. Try to solve it again using a different wording, so instead of subtracting $frac{1}{2}$ cup of the water try subtracting half of the total amount of water, and try the same with the 1/8.

share|cite|improve this answer

answered Jun 7 '16 at 1:50

Discrete MathDiscrete Math

1139

$endgroup$

add a comment | 

$begingroup$

You may be reading the question wrong. Try to solve it again using a different wording, so instead of subtracting $frac{1}{2}$ cup of the water try subtracting half of the total amount of water, and try the same with the 1/8.

share|cite|improve this answer

answered Jun 7 '16 at 1:50

Discrete MathDiscrete Math

1139

$endgroup$

share|cite|improve this answer

answered Jun 7 '16 at 1:50

Discrete MathDiscrete Math

1139

answered Jun 7 '16 at 1:50

Discrete MathDiscrete Math

1139

answered Jun 7 '16 at 1:50

Discrete MathDiscrete Math

1139

2

$begingroup$

Briefly: this question, as presented, is poorly worded.

Less Briefly: you subtracted $frac12$, but you should have multiplied by $1-frac12$ (that is, by $frac12$).

In Detail: the baker poured half "of the water". In ordinary English, we would mean that to mean 'half of the water he had in the measuring cup', not '$frac12$ a cup of water'. If you proceed from here you get the answer $frac78$, which is presumably what was intended.

However, the question then goes on to say that he spilled $frac18$ "of the water" on the floor. Following the logic from before, we would expect this to mean 'an eighth of the water he had in the measuring cup', although this phrase is now itself ambiguous (since it could he 'an eighth of the original amount' or 'an eighth after pouring half'). Neither interpretation gets you an answer on the list, unfortunately.

share|cite|improve this answer

answered Jun 7 '16 at 1:45

Eric StuckyEric Stucky

10.3k32561

$endgroup$

add a comment | 

2

$begingroup$

Briefly: this question, as presented, is poorly worded.

Less Briefly: you subtracted $frac12$, but you should have multiplied by $1-frac12$ (that is, by $frac12$).

In Detail: the baker poured half "of the water". In ordinary English, we would mean that to mean 'half of the water he had in the measuring cup', not '$frac12$ a cup of water'. If you proceed from here you get the answer $frac78$, which is presumably what was intended.

However, the question then goes on to say that he spilled $frac18$ "of the water" on the floor. Following the logic from before, we would expect this to mean 'an eighth of the water he had in the measuring cup', although this phrase is now itself ambiguous (since it could he 'an eighth of the original amount' or 'an eighth after pouring half'). Neither interpretation gets you an answer on the list, unfortunately.

share|cite|improve this answer

answered Jun 7 '16 at 1:45

Eric StuckyEric Stucky

10.3k32561

$endgroup$

add a comment | 

$begingroup$

Briefly: this question, as presented, is poorly worded.

Less Briefly: you subtracted $frac12$, but you should have multiplied by $1-frac12$ (that is, by $frac12$).

In Detail: the baker poured half "of the water". In ordinary English, we would mean that to mean 'half of the water he had in the measuring cup', not '$frac12$ a cup of water'. If you proceed from here you get the answer $frac78$, which is presumably what was intended.

However, the question then goes on to say that he spilled $frac18$ "of the water" on the floor. Following the logic from before, we would expect this to mean 'an eighth of the water he had in the measuring cup', although this phrase is now itself ambiguous (since it could he 'an eighth of the original amount' or 'an eighth after pouring half'). Neither interpretation gets you an answer on the list, unfortunately.

share|cite|improve this answer

answered Jun 7 '16 at 1:45

Eric StuckyEric Stucky

10.3k32561

$endgroup$

share|cite|improve this answer

answered Jun 7 '16 at 1:45

Eric StuckyEric Stucky

10.3k32561

answered Jun 7 '16 at 1:45

Eric StuckyEric Stucky

10.3k32561

answered Jun 7 '16 at 1:45

Eric StuckyEric Stucky

10.3k32561

-1

$begingroup$

I did it like this simply. ( agree wording can be a pain for some)

1.) started with 3/4 and he puts half into batter leaving him with 1/2 of 3/4 = 3/8

2.) he spilled 1/8 on the floor so left with 3/8-1/8 = 2/8 { keep it in this form}

3.) 50% more than he had (3/4) = i do itthis way since we know half of 3/4= 3/8 from above add it to 3/4 = so 3/4 + 3/8 = 9/8

4.) so to get to 9/8 from what he has left 2/8 we need to add back 7/8

share|cite|improve this answer

answered Mar 13 at 3:55

Dizzle DazzleDizzle Dazzle

1

$endgroup$

add a comment | 

-1

$begingroup$

I did it like this simply. ( agree wording can be a pain for some)

1.) started with 3/4 and he puts half into batter leaving him with 1/2 of 3/4 = 3/8

2.) he spilled 1/8 on the floor so left with 3/8-1/8 = 2/8 { keep it in this form}

3.) 50% more than he had (3/4) = i do itthis way since we know half of 3/4= 3/8 from above add it to 3/4 = so 3/4 + 3/8 = 9/8

4.) so to get to 9/8 from what he has left 2/8 we need to add back 7/8

share|cite|improve this answer

answered Mar 13 at 3:55

Dizzle DazzleDizzle Dazzle

1

$endgroup$

add a comment | 

$begingroup$

I did it like this simply. ( agree wording can be a pain for some)

1.) started with 3/4 and he puts half into batter leaving him with 1/2 of 3/4 = 3/8

2.) he spilled 1/8 on the floor so left with 3/8-1/8 = 2/8 { keep it in this form}

3.) 50% more than he had (3/4) = i do itthis way since we know half of 3/4= 3/8 from above add it to 3/4 = so 3/4 + 3/8 = 9/8

4.) so to get to 9/8 from what he has left 2/8 we need to add back 7/8

share|cite|improve this answer

answered Mar 13 at 3:55

Dizzle DazzleDizzle Dazzle

1

$endgroup$

share|cite|improve this answer

answered Mar 13 at 3:55

Dizzle DazzleDizzle Dazzle

1

answered Mar 13 at 3:55

Dizzle DazzleDizzle Dazzle

1

answered Mar 13 at 3:55

Dizzle DazzleDizzle Dazzle

1