suppose that reverend james insists that every person attending easter services make a cash donation to the charity box. there are three choices -- a small donation of $1, a moderate donatio, or a large donation. The large donation is 4 times as much as the moderate donation. if 120 people attend easter service and 50% make a large donation, 20% make a small donation and the rest of the people make a moderate donation, $4440 will be collected. How much money is a moderate donation?

Question

suppose that reverend james insists that every person attending easter services make a cash donation to the charity box.  there are three choices -- a small donation of $1, a moderate donatio, or a large donation.  The large donation is 4 times as much as the moderate donation.  if 120 people attend easter service and 50% make a large donation, 20% make a small donation and the rest of the people make a moderate donation, $4440 will be collected.  How much money is a moderate donation?

anonymous · Answer

Find a new church.

anonymous · Answer

L = size of large donation
M = size of moderate donation
S = size of small donation
60 people make a large donation, 24 people make a small donation, and 36 make a moderate donation, so
24S + 36M + 60L = 4440
S = 1, and L = 4M,
so 24(1) + 36M + 60(4M) = 4440
so 36M + 240M = 4440-24
276M = 4416
M = 4416/276

anonymous · Answer

Ask me about any parts you don't understand. What I did or why I did it.

anonymous · Answer

$16
Solve the following for S, M and L:
{4440=60 L+24S +36M,L=4M,S=1}

anonymous · Answer

how did you get 60 and 36 and 24?

blacksteel · Answer

First we need to find the numbers of people making each kind of donation. 50% made a large donation, so there were 0.5*120 = 60 large donors. 20% made a small donation, so there were 0.2*120 = 24 small donors. Therefore, the remaining number, 120 - 60 - 24 = 36, made a medium donation.

Now let's remove the small donations, since we know how much those were. Those 24 people donated a total of $24. Hence, the remaining 96 people donated a total of $4440 - $24, or $4416.

Let's call the amount of a medium donation M and the amount of a large donation L.
Then we know that 60L + 36M = $4414. We also know that L = 4M. Thus:
60L + 36M = 240M + 36M = 276M = $4416.
Now divide to find M: M = 4414/276 = 16

anonymous · Answer

Lisabel, it tells me that 50% of the congregation gives a large donation and 20% give a small donation. It also tells me that the congregation is 120 in number
to find 50% of 120:
120*.5 =60
to find 20% of 120:
120 * .2 = 24
to find the number of moderate donations (100% - 50% - 20% = 30%) and:
120*.3 = 36

anonymous · Answer

50% of 120, 60, made a large donation.
20% of 120, 24, made a small donation.
120-60-24, 36, made a medium donation.