A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people

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A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is required from the remaining targeted people to complete the fundraising exercise?

A. $200
B. $177.78
C. $100
D. $277.78
E. $377.78

Answer: B

Source: GMAT Paper Tests

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Vincen wrote:
Wed Jul 21, 2021 12:22 pm
A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is required from the remaining targeted people to complete the fundraising exercise?

A. $200
B. $177.78
C. $100
D. $277.78
E. $377.78

Answer: B

Source: GMAT Paper Tests
Let T = the total number of people who will be solicited.
Let B = the total amount required for the new building.

A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations.
In other words: (# of donators)($400 per donor) = 60% of amount needed for building.
Substitute to get: (40% of T)($400) = 60% of B
In other words: (0.4T)(400) = 0.6B

How much average contribution is required from the remaining targeted people to complete the fund raising exercise?
Let C = the required contribution from each remaining person (who hasn't yet donated).
60% of the people have not yet been solicited
They still need to raise the remaining 40% of the total cost of the building
We can write: (# of remaining donators)(C) = 40% of amount needed.
Substitute to get: (60% of T)(C) = 40% of B
In other words: (0.6T)(C) = 0.4B
Solve for C to get: C = (0.4B)/(0.6T) = 4B/6T = (2/3)(B/T)

As we can see, to find the value of C, we need the value of B/T
To do so, we can use the fact that (0.4T)(400) = 0.6B
Divide both sides by 0.4T to get: 400 = 0.6B/0.4T
Multiply numerator and denominator by 10 to get: 400 = 6B/4T
Simplify to get: 400 = 3B/2T
Multiply both sides by 2 to get: 800 = 3B/T
Divide both sides by 3 to get: 800/3 = B/T

Now take C = (2/3)(B/T)
And substitute to get: C = (2/3)(800/3)
Simplify: C = 1600/9 ≈ $177

Answer: B
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