Congratulations to all problem solvers!
Problem 4 Solutions
The correct solution is:
there were 3 girls and 8 boys on the field trip
Solution by Manisha is presented below.
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Name
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Manisha |
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State/Country
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India |
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Age
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15 |
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Solution
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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. |
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Other Interests
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I like Math and dancing. |