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Four brothers Adam, Bill, Charles and David together contributed certain amount of money and purchased a car. The contribution made by Adam is half that of the total contribution made by the other three brothers, contribution made by Bill is one-fourth of the total contribution made by the other three brothers and the contribution made by Charles is two-third of the total contribution made by the other three brothers. If the total price of the car is $9900, find the contribution made by David.
A. $540
B. $580
C. $600
D. $660
E. $680
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We can let the contribution made by Adam, Bill, Charles and David be A, B, C, and D respectively.
Since Adam contributes A dollars, the other three boys contribute 9900 - A dollars; so we have:
A = (1/2)(9900 - A)
2A = 9900 - A
3A = 9900
A = 3,300
Similarly, since Bill contributes B dollars, the other three boys contribute 9900 - B dollars and we have:
B = 1/4(9900 - B)
4B = 9900 - B
5B = 9900
B = 1,980
Finally, since Charles contributed C dollars, the other three boys contributed 9900 - C dollars and thus:
C = 2/3(9900 - C)
3C = 2(9900) - 2C
5C = 2(9900)
C = 3,960
Now that we know A = 3,300, B = 1,980 and C = 3,960, we can easily find D by the following equation:
3,300 + 1,980 + 3,960 + D = 9,900
9,240 + D = 9,900
D = 660
Answer: D