5. A charity conducts a fundraiser. For the first $9,000 raised, Company B will contribute $3 for every $1 raised. For any amount over $9,000, Company B will contribute $1 for every $1 raised. How much must the charity raise to reach a total of $65,000 including Company B's contribution?
Answer: B
The charity must raise $62,000 to reach a total of $65,000 including Company B's contribution.
To achieve a total of $65,000 with Company B's matching contributions, the charity must raise $62,000. This is because Company B contributes $3 for every $1 raised up to $9,000, and $1 for every $1 raised thereafter.
A) $38
Raising $38 would yield a total of $38 + (3 * $38) = $152, which is significantly more than the target of $65,000. Therefore, this option is incorrect.
B) $62,000
By raising $62,000, the charity would receive a contribution of $27,000 from Company B for the first $9,000 raised ($27,000 from B's match) and a contribution of $53,000 for the remaining amount, leading to a total of $65,000. This aligns perfectly with the target.
C) $40
If the charity raises $40, the total contribution would be $40 + (3 * $40) = $160, which also exceeds the required amount of $65,000. Thus, this option is not correct.
E) $42
Raising $42 would result in a total of $42 + (3 * $42) = $168, again far exceeding the target of $65,000. Therefore, this option is incorrect.
G) $49
If the charity raises $49, the total would be $49 + (3 * $49) = $196, which is much more than the required total of $65,000. Hence, this option is also incorrect.
Conclusion
The correct answer is $62,000 because it allows the charity to reach the exact target of $65,000 when combined with Company B's contributions. All other options result in totals that far exceed the required amount, making them invalid choices.