Question 1198175

 man made a will 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 N108 000, what was his wife's share? 
<pre>With {{{4/9}}} going to his wife, {{{matrix(1,3, 1 - 4/9, "=", 5/9)}}} remains
With {{{2/5}}} of the REMAINDER going to the eldest child, {{{matrix(1,5, 3/5, of, 5/9, or, 1/3)}}} remains
With {{{1/3}}} to be shared equally among his 4 younger children, {{{matrix(1,5, 1/3, becomes, (4/4)(1/3), "=", 4/12)}}}. 
Each of the 4 younger children received {{{matrix(1,3, (4/12)/4, "=", 1/12)}}} of the money.
With W being the wife's share, we now get the following proportion: {{{matrix(4,3, (4/9)/(1/12), "=", W/"108,000", (4/9) * 12, "=", W/"108,000", (4/3) * 4, "=", W/"108,000", 16/3, "=", W/"108,000")}}}
                                                                         3W = 16(108,000) ------ Cross-multiplying
 Wife's share, or {{{highlight_green(matrix(1,9, W, "=", 16("108,000")/3, "=", 16("36,000"cross("108,000"))/cross(3), "=", 16("36,000"), "=", highlight("N576,000")))}}}</pre>