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At Roxas Middle School, every student studies Spanish, Chinese, or both Spanish and Chinese. There are 374 students enrolled at the school, and 100  of these students study both Spanish and Chinese. Also, the number of students studying Spanish is twice the number studying Chinese. How many students at Roxas Middle School study Spanish?

So i subtracted 100 from 374 to get 274 but i realized i cannot do that because the students studying both spanish and chinese will be counted in the chinese section and spanish section

 Aug 2, 2022
 #1
avatar+124598 
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Assuming that everyone takes at least one of the subjects :

 

Number in School =   N(Chinese) + N(Spanish) - N (Both)

 

374  =  x  + 2x  - 100

 

474  = 3x

 

x = 474 /  3  =      158  = total taking Chinese

 

2x  = 2 (158)  = 316  = total taking Spanish

 

Proof  (you can set up in a Venn diagram)

 

58 take only Chinese   +   100 take both  +  216 take only Spanish

 

 

cool cool cool

 Aug 2, 2022
 #2
avatar+210 
+1

Thanks! I set up a venn diagram as you said and got the same answer!!

 Aug 2, 2022

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