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Let x be the number of participants;
then the hypothetical number of participants is (x+10).
The cost of the trip for each single participant is .
The cost of trip for each single hypothetical participant is .
The difference in costs is 30, which gives this equation
- = 30. (1)
To solve it, first divide both sides by 30
- = 1. (2)
Now guess the answer MENTALLY: x = 40.
CHECK. - = 5 - 4 = 1. ! Correct !
ANSWER. 40 students took the trip.
Solved.
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Alternatively, you may reduce equation (2) to the standard form quadratic equation and then solve it formally.