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?

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MrRoyal MrRoyal · Answer 1 · 2021-09-22T14:13:22+02:00

The range of a function is the possible output values of the function.

The range of n is between 0 and [tex](x-25) \times (c + 3)[/tex]

Let the number of students be x.

Let the contribution by each student be c

When 10 students left, there are;

[tex]Students = x - 10[/tex]

[tex]Amount = c + 1[/tex]

When 15 students are exempted

[tex]Students =x - 10 - 15[/tex]

[tex]Amount = c + 1 + 2[/tex]

So, we have:

[tex]n = Students \times Amount[/tex]

[tex]n = (x-10 -15) \times (c + 1 + 2)[/tex]

[tex]n = (x-25) \times (c + 3)[/tex]

So, the range of n is between 0 and [tex](x-25) \times (c + 3)[/tex], where

0 represents when no soccer student contributed
[tex](x-25) \times (c + 3)[/tex] represents when all soccer students contributed