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Problem 4 Solutions

The correct solution is:

there were 3 girls and 8 boys on the field trip

Solution by Manisha is presented below.

Name
Manisha
State/Country
India
Age
15
Solution
Let x stand for girls and y stand for boys. The conditions stated in the problem are:
1) x + y < 15
2) 3*x > y
3)2*y > 5 *x
From 2) we conclude that 6*x > 2*y.
Combined with 3) we get 5*x < 2*y < 6*x.
From 5*x < 2*y <6*x we see that x can't be 1, because 5 < 2*y <6 .
If we try x=2, than 10 < 2*y < 12 , the only number that fits is 11, but 2*y must be even number. If we try x=3 , than 15 < 2*y < 18.
From this, the possible answer is 2*y = 16, y = 8.
Now let's check all the 3 conditions from the problem: 1) 3 + 8 < 15 2) 3*3 > 8 3) 2*8 < 5*3 All three conditions are true, so 3 girls and 8 boys is the correct answer.
Other Interests
I like Math and dancing.