Diane find that 5/2 cans of paint are just enough to paint 1/3 of her

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.

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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Other questions based on the unitary method:

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lindsay-can-paint-1-x-of-a-certain-room-in-20-minutes-what-59488.html

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

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.

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

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)

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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IMO answer is D

Given 1/3 room is painted by 5/2 cans of paint
remaining 2/3 room will be painted by 5 cans of paint

Now,How many more cans of paint will she need to finish her room and paint a second room of the same size
=> 5 + 5/2 + 5
=> 25/2
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5/2 can to finish 1/3 room
so 1 room
5/2 / 1/3 = 15/2
and 2/3 of room
15/2 * 2/3 = 5

total required 15/2 + 5
25/2 IMO D

Bunuel are you sure this is a 700 question? I solved it in 41 secs and I can't even solve many 600 questions after 10 mins. This question is very simple. I guess its probably 600-700.

2.5 cans are required to paint 1/3 rd part of the room...

So, 7.5 cans are required to paint the complete room.

Thus, no cans required to finish this room is 5 (ie 7.5 - 2.5) + 7.5 = 12.5

Now, check the options,Answer must be (D) as 25/2 = 12.5
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