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Students in a school agreed to buy a trophy that would be presented to the winning soccer team. Before the trophy was purchased, 10 students left the school, and this meant that all other students had to pay an extra dollar. It was then decided that 15 students who did not play soccer should not contribute to the cost of the trophy. This resulted in the remaining students' cost increasing another $2 each. If the trophy cost $n, in which range is n? (The answers are A)450-699 B)700-949 C)950-1199 D) 1200-1449 E)1450-1699

Respuesta :

N falls within the range of option B which is 700-949

  • Let s be the original number of students and let c be the cost for each student initially.

The trophy costs $n. Thus;

sc = n  - - - (eq 1)

  • Now, 10 students left the school and each student had to pay an extra dollar to meet up with the cost of the trophy. Thus;

(s - 10)(c + 1) = n

sc - 10c + s - 10 = n   - - - (eq 2)

  • We are told that 15 students who did not play soccer should not contribute to the cost of the trophy which meant that students' cost increased by another $2 each. Thus;

(s - 10 - 15)(c + 1 + 2) = n

(s - 25)(c + 3) = n

sc - 25c + 3s - 75 = n - - - (eq 3)

  • From eq 1, sc = n. Putting n for sc in eq 2 and 3 and simplifying, we have;

s - 10c = 10 - - - (eq 4)

3s - 25c = 75  - - - (eq 5)

  • Multiply eq 4 by -3 and eq 5 by 1 and add them to get;

30c - 25c = -30 + 75

5c = 45

c = 45/5

c = $9

  • Put 9 for c in s - 10c = 10 to get;

s - 10(9) = 10

s - 90 = 10

s = 10 + 90

s = 100

  • Since n = sc

Thus; n = 100 × 9 = $900

Looking at the options, n falls in the range of option B which is 700-949

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