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Question 1210724: A community center hosts an art program with a total of 420 participants divided into three workshops (Painting, Sculpture, and Ceramics). 2/7 of the total participants are in the Painting workshop. 35% of the total participants are in the Sculpture workshop. The remaining participants are in the Ceramics workshop, which is split into two classes—Glazing and Handbuilding—in the ratio of 4 : 5 respectively. How many participants are in the Handbuilding class?
Answer by ikleyn(54062)   (Show Source):
You can put this solution on YOUR website! .
A community center hosts an art program with a total of 420 participants divided into three workshops
(Painting, Sculpture, and Ceramics).
2/7 of the total participants are in the Painting workshop.
35% of the total participants are in the Sculpture workshop.
The remaining participants are in the Ceramics workshop,
which is split into two classes—Glazing and Handbuilding—in the ratio of 4 : 5 respectively.
How many participants are in the Handbuilding class?
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It has a simple arithmetic solution.
2/7 of 420 is  = 120.
35% of 420 is 420*0.35 = 147.
So, the total in the Ceramic workshop is 420 - 120 - 147 = 153 participants.
We should split 153 in the ratio 4 : 5.
So, there are 4 + 5 = 9 equal parts, and 153/9 = 17 participants in each part.
Hence, the number of participants in the Handbuilding class is 5 times 17, or 85.
ANSWER. There are 85 participants in the Handbuilding class.
Solved completely.
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