Question 936145
Let {{{ s }}} = Sarah's age now
Let {{{ r }}} = Ruth's age now
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(1) {{{ s = 3r - 14 }}}
(2) {{{  sqrt( s + 1 ) = sqrt( r + 15 ) }}}
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Square both sides of (2)
(2) {{{ s + 1 = r + 15 }}}
(2) {{{ s - r = 14 }}}
and, from (1):
(1) {{{ -s + 3r = 14 }}}
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Add the equations
(2) {{{ s - r = 14 }}}
(1) {{{ -s + 3r = 14 }}}
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{{{ 2r = 28 }}}
{{{ r = 14 }}}
and, since
(1) {{{ s = 3r - 14 }}}
(1) {{{ s = 3*14 - 14 }}}
(1) {{{ s = 28 }}}
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Ruth is 14
Sarah is 28
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check:
(2) {{{  sqrt( s + 1 ) = sqrt( r + 15 ) }}}
(2) {{{  sqrt( 28 + 1 ) = sqrt( 14 + 15 ) }}}
(2) {{{ sqrt(29) = sqrt(29) }}}
OK
(1) {{{ s = 3r - 14 }}}
(1) {{{ 28 = 3*14 - 14 }}}
(1) {{{ 28 = 42 - 14 }}}
(1) {{{ 28 = 28 }}}
OK
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