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Diane find 2 and a half cans of paint are just enough to

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Diane find 2 and a half cans of paint are just enough to  [#permalink]

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New post 16 Feb 2013, 12:40
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Diane find 2 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?

A. 5
B. 7 and a half
C. 10
D. 12 and a half
E. 15
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Re: Diane find 2 and a half cans of paint are just........  [#permalink]

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New post 16 Feb 2013, 22:27
She will need 5 cans to paint the rest of this room and seven and a half for the next room for a total of twleve and half cans.

D it is.
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Re: Diane find 2 and a half cans of paint are just........  [#permalink]

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New post 18 Feb 2013, 21:10
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antoxavier wrote:
Diane find 2 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?

A. 5
B. 7 and a half
C. 10
D. 12 and a half
E. 15


Notice that for 1/3 of a room, she used 2.5 cans.
For 2 full rooms (i.e. 6 times the initial work), she will need a total of 2.5 * 6 = 15 cans

So she needs 15 - 2.5 = 12.5 more cans to finish her room and paint another room of the same size.
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Re: Diane find 2 and a half cans of paint are just enough to  [#permalink]

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New post 04 Mar 2013, 21:56
Other questions based on the unitary method:

if-sally-can-paint-a-house-in-4-hours-and-john-can-paint-141777.html
lindsay-can-paint-1-x-of-a-certain-room-in-20-minutes-what-59488.html
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Re: Diane find 2 and a half cans of paint are just enough to  [#permalink]

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New post 07 Dec 2014, 12:55
We can use ratios to solve this problem:
We know that 2.5 cans = 25/10 is used to paint 1/3 of a room. We need to find how much paint we'll need in order to paint the rest of the room (1-1/3=2/3) and 1 room more, hence 2/3+1=5/3

25/10 : 1/3 = x : 5/3

(25/10)*(5/3) = (1/3)*x
25/6=x/3
6*x=25*3
x=75/6
x=12.5
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Re: Diane find 2 and a half cans of paint are just enough to  [#permalink]

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New post 13 Mar 2016, 06:52
To do this problem we can pick a convenient number. Let us say the total room is 9 parts. To do 3 parts She needs 2.5. To do the next 6, she needs 5. Then to do all 9 she needs 7.5. So total required cans are 7.5+5=12.5.
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Re: Diane find 2 and a half cans of paint are just enough to  [#permalink]

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New post 13 Mar 2016, 07:53
antoxavier wrote:
Diane find 2 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?

A. 5
B. 7 and a half
C. 10
D. 12 and a half
E. 15

Diane has to finish painting two rooms of 6 parts, each part equal to one-third of a room.
For 1 part she needs 2 and a half cans of paint.
For another 5 parts she needs 5*2.5=12.5 cans
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Diane find 2 and a half cans of paint are just enough to  [#permalink]

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New post 09 Aug 2017, 04:21
5/2 cans paint 1/3 of the room

1 can paints 2/15 of the room --> to paint a room she needs 7.5 cans

She'll need 5 more cans to paint remaining of the room and another 7.5 cans to paint the second room

Total 12.5 cans (Choice D)
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Diane find 2 and a half cans of paint are just enough to  [#permalink]

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New post 09 Aug 2017, 14:27
antoxavier wrote:
Diane find 2 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?

A. 5
B. 7 and a half
C. 10
D. 12 and a half
E. 15

Proportion with multiplier approach

Remaining work = \(\frac{5}{3}\)
Let x = amount of paint needed

\(\frac{\frac{5}{2}}{\frac{1}{3}}\) = \(\frac{x}{\frac{5}{3}}\)

Use the multiplier for the denominator:
\(\frac{1}{3}\) ---> \(\frac{5}{3}\) means \(\frac{1}{3}\) was multiplied by 5.

So multiply the numerator by 5.
\(\frac{5}{2}\) * 5 = \(\frac{25}{2}\) or 12\(\frac{1}{2}\)

Answer D

Straight proportion method

Remaining work: \(\frac{5}{3}\)
Let x = amount of paint needed

\(\frac{\frac{5}{2}}{\frac{1}{3}}\) = \(\frac{x}{\frac{5}{3}}\)

\(\frac{1}{3}\)x = \(\frac{5}{2}\) * \(\frac{5}{3}\)

\(\frac{1}{3}\)x = \(\frac{25}{6}\)

x = \(\frac{25}{6}\) * 3

x = \(\frac{25}{2}\) or 12\(\frac{1}{2}\)

Answer D
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