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12 Mar 2025, 21:53
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Event Y: $3,000
Event Z: $2,000
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Difficulty:
5%
(low)
Question Stats:
95% (01:34) correct
5%
(01:22)
wrong
based on 408
sessions
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The board of directors for a philanthropic organization is allocating funds for the three fund-raising events they plan to hold next year: Events X, Y, and Z. The organizers of the events have requested that the following amounts be allocated to the events:
Event X: $12,000
Event Y: $5,000
Event Z: $3,000
The board has a total budget of $15,000 for the three events, and they will distribute all of the $15,000 among the 3 events. Each event will receive at most the requested amount and at least half the requested amount.
If the board allocates $10,000 to Event X, select for Event Y and for Event Z amounts the board could allocate to Event Y and Event Z, respectively, so that the amounts would jointly adhere to the constraints described above. Make only two selections, one in each column.
Event X: $12,000
Event Y: $5,000
Event Z: $3,000
The board has a total budget of $15,000 for the three events, and they will distribute all of the $15,000 among the 3 events. Each event will receive at most the requested amount and at least half the requested amount.
If the board allocates $10,000 to Event X, select for Event Y and for Event Z amounts the board could allocate to Event Y and Event Z, respectively, so that the amounts would jointly adhere to the constraints described above. Make only two selections, one in each column.
| Event Y | Event Z | |
| $1,000 | ||
| $2,000 | ||
| $3,000 | ||
| $4,000 | ||
| $5,000 |
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Official Answer
Event Y: $3,000
Event Z: $2,000
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13 Mar 2025, 05:57
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Solution:
It has already been mentioned in the question stem that the board has a total budget of $15,000 for the three events, and they will distribute all of the $15,000 among the 3 events. Each event will receive at most and at least half the requested amount.
The board allocates $10000 to Event X
As we know Event X: $12,000
Event Y: $5,000
Event Z: $3,000
If we subtract $10000 from $15000 we will left with $5000. This amount is to be distributed between Event Y and Z. So, the only feasible option we are left with is $2000 for Event Z and $3000 for Event Y.
It has already been mentioned in the question stem that the board has a total budget of $15,000 for the three events, and they will distribute all of the $15,000 among the 3 events. Each event will receive at most and at least half the requested amount.
The board allocates $10000 to Event X
As we know Event X: $12,000
Event Y: $5,000
Event Z: $3,000
If we subtract $10000 from $15000 we will left with $5000. This amount is to be distributed between Event Y and Z. So, the only feasible option we are left with is $2000 for Event Z and $3000 for Event Y.
Bismuth83
13 Mar 2025, 22:00
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1. We're asked to find exactly how much of the budget was distributed among Events Y and Z.
2. Let a and b be how much is spent on Events Y and Z, respectively. The restrictions tell us that \(2500 \leq a \leq 5000\) and \(1500 \leq b \leq 3000\).
3. It is also known that the total budget was 15000, so, \(15000 = 10000 + a + b \rightarrow b = 5000 - a\). Our 2nd inequality will turn into \(1500 \leq 5000 - a \leq 3000 \rightarrow -3500 \leq -a \leq -2000 \rightarrow 2000 \leq a \leq 3500\).
4. Then, we know that \(2500 \leq a \leq 3500\). The only answer that's in this range is a = 3000, which means b = 2000.
5. Our answer will be: Event Y - $3,000 and Event Z - $2,000.
2. Let a and b be how much is spent on Events Y and Z, respectively. The restrictions tell us that \(2500 \leq a \leq 5000\) and \(1500 \leq b \leq 3000\).
3. It is also known that the total budget was 15000, so, \(15000 = 10000 + a + b \rightarrow b = 5000 - a\). Our 2nd inequality will turn into \(1500 \leq 5000 - a \leq 3000 \rightarrow -3500 \leq -a \leq -2000 \rightarrow 2000 \leq a \leq 3500\).
4. Then, we know that \(2500 \leq a \leq 3500\). The only answer that's in this range is a = 3000, which means b = 2000.
5. Our answer will be: Event Y - $3,000 and Event Z - $2,000.
