SOLUTION: Hi A B C and D donated $900.00 . A contributed 20% of the total sum donated by her 3 friends. B contributed 25% of the total sum donated by her 3 friends. C contributed 50% of the

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Question 1205552: Hi
A B C and D donated $900.00 . A contributed 20% of the total sum donated by her 3 friends. B contributed 25% of the total sum donated by her 3 friends. C contributed 50% of the total sum donated by her friends. What percentage of the total sum donated by the 4 friends did D contribute.

Found 3 solutions by josgarithmetic, greenestamps, math_tutor2020:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Not the complete solution; just an approach: 
A                   (1/5)(B+C+D)

B                   (1/4)(A+C+D)

C                   (1/2)(A+B+D)

D                         D

TOTAL                      900

system%28A%2BB%2BC%2BD=900%2C5A=B%2BC%2BD%2C4B=A%2BC%2BD%2C2C=A%2BB%2BD%29


Simple linear operations are seeming to show this:
system%286A=900%2C5B=900%2C3C=900%29
.
.
.
D gave 30%,

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


A different approach than the good one outlined by the other tutor....

Since A contributed 20% of the total contributed by the others, the fraction of the total that A contributed was 20%2F%2820%2B100%29=20%2F120=1%2F6.

Similarly, since B contributed 25% of the total contributed by the others, the fraction of the total B contributed was 25%2F%2825%2B100%29=25%2F125=1%2F5.

And since C contributed 50% of the total contributed by the others, the fraction of the total B contributed was 50%2F%28505%2B100%29=50%2F150=1%2F3.

So A contributed 1/6 of $900, or $150; B contributed 1/5 of $900, or $180; and C contributed 1/3 of $900, or $300.

Their combined contributions were $150+$180+$300 = $630, so the amount D contributed was $900-$630 = $270, which is 270/900 = 3/10 or 30% of the total.

ANSWER: 30%

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Refer to the equations that tutor josgarithmetic set up.
For now the 1st two equations are what we focus on.
A+B+C+D = 900
5A = B+C+D

Notice that both involve B+C+D
We can replace B+C+D in the 1st equation with 5A
The 1st equation turns into A+5A = 900 and that solves to A = 150.

Follow similar steps to determine B and C.


You should have the following
A = 150
B = 180
C = 300
That must mean D = 900-A-B-C = 900-150-180-300 = 270

Lastly, D/900 = 270/900 = 0.30 = 30%


Answer: D contributed 30% of the total funds.