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At a certain gallery, the ratio of the number of sculptures to the num
[#permalink]
12 Aug 2022, 03:17
12 Aug 2022, 03:17
Expert Reply
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Question Stats:
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At a certain gallery, the ratio of the number of sculptures to the number of paintings is 1 to 2. If 45 sculptures were added to the gallery the ratio of the number of sculptures to the number of paintings would be 2 to 1. The total number of sculptures and paintings in the gallery is
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
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Joined: 25 Mar 2022
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Re: At a certain gallery, the ratio of the number of sculptures to the num
[#permalink]
12 Aug 2022, 09:22
12 Aug 2022, 09:22
Formulated this way, is the question implying "prior to adding 45 sculptures" or is it after having added them?
Re: At a certain gallery, the ratio of the number of sculptures to the num
[#permalink]
12 Aug 2022, 09:46
12 Aug 2022, 09:46
Expert Reply
Bunuel wrote:
At a certain gallery, the ratio of the number of sculptures to the number of paintings is 1 to 2. If 45 sculptures were added to the gallery the ratio of the number of sculptures to the number of paintings would be 2 to 1. The total number of sculptures and paintings in the gallery is
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
(A) 30
(B) 45
(C) 60
(D) 75
(E) 90
"the ratio of the number of sculptures to the number of paintings is 1 to 2"
2S=P
"If 45 sculptures were added to the gallery the ratio of the number of sculptures to the number of paintings would be 2 to 1."
S+45 = 2P
Multiply the first equation by 2
4S=2P
Substitute 4S for 2P in the second equation
S+45 = 4S
45 = 3S
S = 15
Plug S=15 into the first equation
2(15) = P
P = 30
15+30 = 45
Answer choice B.
