Three people of kaui Island are named Alice, Bob and Carol. At least one of them is a Knight and at least one is a Knave. Exactl
1 answer:
Answer: Alice has the prize
<u>Step-by-step explanation:</u>
Line 1:
Alice: Bob doesn’t have the prize (T) ... either Alice or Carol
Bob: I don’t have the prize (T) ... either Alice or Carol
Carol: I have the prize (F) ... either Alice or Bob
Alice is true for all of them!
Line 2:
Alice: Bob doesn’t have the prize (T) ... either Alice or Carol
Bob: I don’t have the prize (F) ... Bob
Carol: I have the prize (F) ... either Alice or Bob
<em>nobody satisfies all three statements.</em>
Line 3:
Alice: Bob doesn’t have the prize (T) ... either Alice or Carol
Bob: I don’t have the prize (F) ... Bob
Carol: I have the prize (T) ... Carol
<em>nobody satisfies all three statements.</em>
Line 4:
Alice: Bob doesn’t have the prize (F) ... Bob
Bob: I don’t have the prize (T) ... either Alice or Carol
Carol: I have the prize (T) ... Carol
<em>nobody satisfies all three statements.</em>
<em />
Line 5:
Alice: Bob doesn’t have the prize (F) ... Bob
Bob: I don’t have the prize (F) ... Bob
Carol: I have the prize (T) ... Carol
<em>nobody satisfies all three statements.</em>
<em />
Line 6:
Alice: Bob doesn’t have the prize (F) ... Bob
Bob: I don’t have the prize (T) ... either Alice or Carol
Carol: I have the prize (F) ... either Alice or Bob
<em>nobody satisfies all three statements.</em>
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G = number of girls taking the martial arts classes
and
B = number of boys taking the martial arts classes
We know that for every girl, there are 3 boys. Therefore, the proportion of girls to boys is:
= 
When you simplify this ratio by cross-multiplying you get:
3G = B
When you think about this, it makes sense because you know that there are 3 times as many boys as there are girls. Therefore you would need to multiply the number of girls by 3 to equal the number of boys in the class.
We know that there are 236 total people in the class, Therefore we know that:
G + B = 236
You can replace the B in the equation above with your simplified ratio to solve, since both contain the variable B:
G + B = 236
is the same as
G + 3G = 236 ->
4G = 236 ->
G = 59
So there are 59 girls in the class, but you need to figure out the number of boys, not girls. Therefore, subtract 59 from 236 to get to the final answer:
G + B = 236
59 + B = 236
59 + B - 59 = 236 - 59
B = 177
and
B = number of boys taking the martial arts classes
We know that for every girl, there are 3 boys. Therefore, the proportion of girls to boys is:
When you simplify this ratio by cross-multiplying you get:
3G = B
When you think about this, it makes sense because you know that there are 3 times as many boys as there are girls. Therefore you would need to multiply the number of girls by 3 to equal the number of boys in the class.
We know that there are 236 total people in the class, Therefore we know that:
G + B = 236
You can replace the B in the equation above with your simplified ratio to solve, since both contain the variable B:
G + B = 236
is the same as
G + 3G = 236 ->
4G = 236 ->
G = 59
So there are 59 girls in the class, but you need to figure out the number of boys, not girls. Therefore, subtract 59 from 236 to get to the final answer:
G + B = 236
59 + B = 236
59 + B - 59 = 236 - 59
B = 177
Answer:AA~
Step-by-step explanation:
