Question 1168227

a man leaves 60000$to his children and grandchildren, seven in all. the children receive 1/3 of it, which is 2000 more a piece than the grandchildren get. how much is the amount received by the grandchildren
<pre>Let number of grandchildren be G
Then number of children = 7 - G
We then get the following equation: {{{matrix(1,3, "20,000"/(7 - G) - "2,000", "=", "40,000"/G)}}}
20,000G - 2,000G(7 - G) = 40,000(7 - G) ----- Multiplying by LCD, G(7 - G)
{{{matrix(3,3, "2,000"G^2 + "46,000"G - "280,000", "=", 0, "2,000"(G^2 + 23G - 140), "=", "2,000"(0), G^2 + 23G - 140, "=", 0)}}}
(G - 5)(G + 28) = 0
Number of grandchildren, or {{{highlight_green(matrix(1,3, G, "=", 5))}}}    OR G = - 28 (ignore)