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Difficulty: 505-555 Level,   Fractions and Ratios,   Mixture Problems,                        
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
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AbdurRakib wrote:
Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups

OG Q 2017 (Book Question: 59)


9/4 - 4/3 = 11/12

11/12 is very close to 1 but is <1. It falls in the range that choice C mentions
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
AbdurRakib wrote:
Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups

OG Q 2017 (Book Question: 59)


(9/4) - 2*(2/3) = 11/12 which is more than 3/4 and less than 1.
Ans is Choice C)

Good luck
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
(9/4)-2(2/3)
(9/4)-(4/3)
11/12 ~0.9

C is the correct answer.
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Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
AbdurRakib wrote:
Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups

OG Q 2017 (Book Question: 59)



why is my solution wrong ? :-)

\(\frac{9}{4}\) * \(\frac{2}{3}\) = \(\frac{3}{2}\)

\(\frac{9}{4}\) - \(\frac{3}{2}\) = \(\frac{3}{4}\)

\(\frac{3}{4}\) * \(\frac{2}{3}\) = \(\frac{1}{2}\)

\(\frac{3}{2}\) + \(\frac{1}{2}\) =\(\frac{4}{2}\)

\(\frac{9}{4}\) - \(\frac{4}{2}\) = \(\frac{1}{4}\)

final answer i get \(\frac{1}{4}\)
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Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
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dave13 wrote:
AbdurRakib wrote:
Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups

OG Q 2017 (Book Question: 59)



why is my solution wrong ? :-)

\(\frac{9}{4}\) * \(\frac{2}{3}\) = \(\frac{3}{2}\)

\(\frac{9}{4}\) - \(\frac{3}{2}\) = \(\frac{3}{4}\)

\(\frac{3}{4}\) * \(\frac{2}{3}\) = \(\frac{1}{2}\)

\(\frac{3}{2}\) + \(\frac{1}{2}\) =\(\frac{4}{2}\)

\(\frac{9}{4}\) - \(\frac{4}{2}\) = \(\frac{1}{4}\)

final answer i get \(\frac{1}{4}\)


Hi dave13

Where you are making a mistake is by dividing the total milk by \(\frac{2}{3}\)rd?

What the question is saying is that \(\frac{2}{3}\)rd cup is used for each batch
of cookies and Stephanie bakes 2 batches of cookies.

So, Stephanie uses \(\frac{2}{3}\)+\(\frac{2}{3}\)rd or \(\frac{4}{3}\)rd cups of milk.

In total, she had \(\frac{9}{4}\) cups of milk and she will be left with \(\frac{9}{4}\) - \(\frac{4}{3}\) = \(\frac{11}{12}\) cups

So, the answer is Option C(between \(\frac{3}{4}\)cup and 1 cup)

Hope that helps you!
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
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AbdurRakib wrote:
Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups


Since each batch of cookies requires 2/3 cup of milk, two batches require 2 x 2/3 = 4/3 cups of milk. So after Stephanie makes two batches of cookies, she has

9/4 - 4/3 = 27/12 - 16/12 = 11/12

cups of milk left.

Answer: C
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
2/3 cup of milk for 1 batch
(2/3 + 2/3)=4/3 cup of milk for 2 batches of cookies
So
Remaining milk = 9/4 - 4/3 = 11/12
As 11/12 is between 3/4 and 1 so answer is (C)

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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
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AbdurRakib wrote:
Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups

OG Q 2017 (Book Question: 59)


\(\frac{9}{4} - \frac{2}{3} = \frac{27}{12} - \frac{8}{12}*2 = \frac{27}{12} - \frac{16}{12} = \frac{11}{12}\)

Answer choice C
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Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
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Two methods to solve:

Method 1 - Fractions

9/4 - 2*2/3
=9/4 -4/3
= 11/12
1/12 ~0.08
11*0.08 = 0.96

Or alternatively just recognise that 11/12 is just a bit less than 1

Method 2 - Decimals

2 1/4 =2.25
- 4/3 = 1.33
=0.92
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
9/4 - 2*2/3 = 11/12 = 0.9
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
Top Contributor
AbdurRakib wrote:
Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups

OG Q 2017 (Book Question: 59)


\(\frac{2}{3}\)*2=\(\frac{4}{3}\) for two cups

Left:
\(\frac{9}{4}\)-\(\frac{4}{3}\)=\(\frac{11}{12}\), which less than 1 but more 0.9

The answer is C
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
I took a visual approach
There are 3 cups A=1, B=1, C=1/4 (1+1+1/4 = 9/4)
Now removing 2/3 from cup A and 2/3 from cup B

Remaining milk - A=1/3, B=1/3, C=1/4
Adding - A+B =2/3, C=1/4
Since 1/4<1/3
2/3+1/4 <1 (sum will be less than 1 OR sum will be 1 only when 2/3+1/3=1) - Reject D, E

Remaining milk A+B =2/3, C=1/4
Milk left will be more than 1/2 since 2/3 (66%) >1/2(50%) - Reject A
To arrive at 3/4<2/3+1/4
Compare the difference with 2/3-3/4=1/12
1/12< 1/4 or 1/12<3/12
So 3/4<2/3+1/4
The answer is C
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
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pushpitkc wrote:
dave13 wrote:
AbdurRakib wrote:
Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?

A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups

OG Q 2017 (Book Question: 59)



why is my solution wrong ? :-)

\(\frac{9}{4}\) * \(\frac{2}{3}\) = \(\frac{3}{2}\)

\(\frac{9}{4}\) - \(\frac{3}{2}\) = \(\frac{3}{4}\)

\(\frac{3}{4}\) * \(\frac{2}{3}\) = \(\frac{1}{2}\)

\(\frac{3}{2}\) + \(\frac{1}{2}\) =\(\frac{4}{2}\)

\(\frac{9}{4}\) - \(\frac{4}{2}\) = \(\frac{1}{4}\)

final answer i get \(\frac{1}{4}\)


Hi dave13

Where you are making a mistake is by dividing the total milk by \(\frac{2}{3}\)rd?

What the question is saying is that \(\frac{2}{3}\)rd cup is used for each batch
of cookies and Stephanie bakes 2 batches of cookies.

So, Stephanie uses \(\frac{2}{3}\)+\(\frac{2}{3}\)rd or \(\frac{4}{3}\)rd cups of milk.

In total, she had \(\frac{9}{4}\) cups of milk and she will be left with \(\frac{9}{4}\) - \(\frac{4}{3}\) = \(\frac{11}{12}\) cups

So, the answer is Option C(between \(\frac{3}{4}\)cup and 1 cup)

Hope that helps you!


Dear pushpitkc
the mistake that dave13 outlined is because he took part from the whole and then part from the remainder. The same as we take 1 cup and then portion of cup in lieu of 2 full cups.

From question stem: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cups of milk for each batch of cookies

That is 2/3 Cups OF Milk is not the same as 2/3 cups OF 9/4

Thus, the solution will be 9/4 cups - 2 * 2/3 cups = 9/4 - 4/3 = 11/12

Hope it helps.
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Re: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, [#permalink]
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