Question 1150819
A man made a will the in which he left  4/9 of his money to his wife and 2/5 of the remainder to his eldest child. The rest was to be shared equally among his four younger children. If each of the younger children received $108000; what was his wife's share? 
<pre>Fraction wife received: {{{4/9}}}
Fraction eldest child received: {{{matrix(1,7, (2/5) * (1 - 4/9), "=", (2/5) * (5/9), "=", (2/cross(5)) * (cross(5)/9), "=", 2/9)}}}
Fraction ALL four younger children received: {{{matrix(1,7, 1 - (4/9 + 2/9), "=", 1 - 6/9, "=", 3/9, or, 1/3)}}}
Fraction each of the four younger children received: {{{matrix(1,3, (1/3)/4, "=", 1/12)}}}
With each of the four younger children receiving {{{1/12}}}, or $108,000, and the wife's share being W, we get the following PROPORTION and wife's (W's) share: {{{highlight_green(matrix(1,23, (1/12)/(4/9), "=", "108,000"/W, "=====>", (1/12) * (9/4), "=", "108,000"/W, "====>", 3/16, "=", "108,000"/W, "=====>", (3/16)W, "=", "108,000", "=====>", highlight(W), "=", ("108,000")/(3/16), "=", "108,000" * (16/3), "=", highlight("$576,000")))}}}