Question 1046396
Let {{{ a }}} = number of beads that Anna 
had originally
Let {{{ b }}} = number of beads that Zoe
had originally
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(1) {{{ a = 3b }}}
(2) {{{ a + b = 480 }}}
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{{{ 3b + b = 480 }}}
{{{ 4b = 480 }}}
{{{ b = 120 }}}
and
(1) {{{ a = 3b }}}
(1) {{{ a = 3*120 }}}
(1) {{{ a = 360 }}}
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Let {{{ n }}} = the equal number of beads
that mrs Taylor then gave them
(3) {{{ b + n = (1/2)*(  a + n ) }}}
(3) {{{ 2b + 2n = a + n }}}
(3) {{{ n = a - 2b }}}
(3) {{{ n = 360 - 2*120 }}}
(3) {{{ n = 360 - 240 }}}
(3) {{{ n = 120 }}}
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{{{ b +n = 120 + 120 = 240 }}}
and
{{{ a + n = 360 + 120 = 480 }}}
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Mrs Taylor gave Anna 480 beads
She gave Zoe 240 beads
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check:
(3) {{{ b + n = (1/2)*(  a + n ) }}}
(3) {{{ 120 + 120 = (1/2)*(  360 + 120 ) }}}
(3) {{{ 240 = (1/2)*480 }}}
(3) {{{ 480 = 480 }}}
OK