3. 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, the charity needs to raise a specific amount that, when combined with Company B’s contributions, equals the target. For the first $9,000, Company B contributes $3 for every $1 raised, resulting in a significant contribution. Beyond that, the contribution rate changes to $1 for every $1 raised.
A) $38
Raising $38 would only yield a total of $38 + ($3 * $38) = $152, which is far less than the target of $65,000. This option is not viable as it does not approach the required total.
B) $62,000
If the charity raises $62,000, the calculation would be $9,000 raised initially, leading to a contribution of $27,000 from Company B. The remaining amount raised ($62,000 - $9,000 = $53,000) would receive a 1:1 contribution, totaling an additional $53,000. Thus, the total raised would be $62,000 + $27,000 + $53,000 = $65,000, making this the correct answer.
C) $40
A total raised of $40 would result in $40 + ($3 * $40) = $160. This amount is insufficient as it does not come close to the required total of $65,000. Therefore, this option is incorrect.
D) $49
Raising $49 would lead to a total of $49 + ($3 * $49) = $196. Like the previous options, this amount is far below the necessary total of $65,000, rendering this choice invalid.
E) $42
If the charity raises $42, the total would be $42 + ($3 * $42) = $168. This amount is inadequate in reaching the target of $65,000, thus making this option incorrect.
G) $49
Raising $49 would result in $49 + ($3 * $49) = $196. This total is also insufficient to meet the goal of $65,000, confirming this option as incorrect.
Conclusion
In conclusion, the charity must raise $62,000 to reach a total of $65,000 when including Company B’s contributions. This calculation is supported by the breakdown of contributions for the first $9,000 and the subsequent rate for any amount raised above this threshold. All other options fall significantly short of the required total, confirming that they are not feasible solutions.