The question involves arithmetic sequences. The first brother gets 5.5 gold coins with subsequent brothers getting 1 more coin than the brother before them. This gradually increases to the tenth brother who gets 14.5 gold coins.
This problem involves the concept of arithmetic sequences where each term is a constant amount different from the previous term. Given the seventh oldest brother receives 7 gold coins, we can denote the amount of money the first brother gets as x. The increment in each sequential brother's amount is then 1.
Firstly, denote the amount of money the first brother gets as x. Since each subsequent brother gets 1 more gold coin, we can denote the amount the other brothers receive as follows: x, x+1, x+2, ..., x+6 (for the seventh brother), ..., x+9 (for the tenth brother).
As the problem states that the total gold the brothers receive is 100, you would set up the equation: 10x + 45 = 100, where 45 is the sum of the increments from 1 to 9. Solving this equation for x, we get x=5.5. This means the first brother received 5.5 gold coins and each subsequent brother received 1 more than his immediate predecessor.
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A.
–$70,000
B.
$114,000
C.
$44,000
D.
–$44,000
Q(−5, 8), S(1, −3)
Q(5, −8), S(−1, 3)
Q(−5, −8), S(1, 3)
Q(−5, 8), S(−1, 3)