The cost of a class picnic was 42 If 14 more students had co

The cost of a class picnic was $42. If 14 more students had come, the cost per student would have been 20 cents less. How much is the cost per student?

Solution

Let original number of students is \"x\".
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Original cost per student = 42/x dollars
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When 14 students are added the cost per student = 42/(x+14)
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Equation:
original cost per student - new cost per student = 1/5 dollar
42/x - 42/(x+14) = 1/5
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Multiply thru by 5x(x+14) to get:
42*5(x+14) - 42*5x = x(x+14)
210x + 210*14 - 210x = x^2 + 14x
x^2 + 14x - 2940 = 0
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x = [-14 +- sqrt(14^2 - 4*1*-2940)]/2
x = 47.67