SOLUTION: A grade 11 class, on a field trip to Montreal, had lunch in a restaurant. The bill came to $239.25. Four students had birthdays that day, and it was agreed that these four students

Question 135103: A grade 11 class, on a field trip to Montreal, had lunch in a restaurant. The bill came to $239.25. Four students had birthdays that day, and it was agreed that these four students should not have to pay for lunch. The other students had to pay $1 more than if all the students had paid. How many students had lunch?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A grade 11 class, on a field trip to Montreal, had lunch in a restaurant. The bill came to $239.25. Four students had birthdays that day, and it was agreed that these four students should not have to pay for lunch. The other students had to pay $1 more than if all the students had paid. How many students had lunch?
:
Let x = no. of students that had lunch
then
(x-4) = no. of students that paid
:
Cost per student if all paid =
and
Cost per student that actually paid =
:
If All paid cost + $1 = Actual paid cost
+ 1 =
:
Multiply equation by x(x-4) to eliminate the denominators, results:
239.25(x-4) + x(x-4) = 239.25x
:
239.25x - 957 + x^2 - 4x = 239.25x
:
x^2 + 239.25x - 239.25x - 4x - 957 = 0: combine like terms on the left
:
x^2 - 4x - 957 = 0; a quadratic equation
Factors to:
(x-33)(x+29) = 0
:
x = +33 Students in the group (ignore the neg solution)
;
;
Check solution by finding the costs:
+ 1 =
7.25 + 1 = 8.25

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