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

## 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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Let T = the total number of people who will be solicited.Vincen wrote: ↑Wed Jul 21, 2021 12:22 pmA 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 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