Question 670548
Let {{{ n }}} = the number of children she has
Let {{{ A }}} = the amount of money she has
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In the 1st case, she gives her children:
(1) {{{A =  .11n + .09 }}}
In the 2nd case, she gives them each:
(2) {{{ ( A + .47 ) / n = .15 }}}
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(2) {{{ A + .47 = .15n }}}
(2) {{{ A = .15n - .47 }}}
substitute (1) into (2)
(2) {{{ .11n + .09 = .15n - .47 }}}
(2) {{{ .04n = .56 }}}
(2) {{{ n = 14 }}}
She has 14 children
and
(1) {{{A =  .11*14 + .09 }}}
(1) {{{ A = 1.54 + .09 }}}
(1) {{{ A = 1.63 }}}
She has $1.63
check answer:
{{{ 1.63 / 14 = .11 + .09/14 }}}
{{{ 1.63 = 1.54 + .09 }}}
{{{ 1.63 = 1.63 }}}
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(2) {{{ A + .47 = .15n }}}
(2) {{{ 1.63 + .47 = .15*14 }}}
(2) {{{ 2.1 = 2.1 }}}
OK