Question 1050058
Let {{{ a }}} = Jose's age now
Let {{{ b }}} = Maria's age now
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(1) {{{ a - 2 = (5/2)*( b - 2 ) }}}
(2) {{{ a + 10 = (3/2)*( b + 10 ) }}}
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(1) {{{ 2a - 4 = 5*( b-2 ) }}}
(1) {{{ 2a - 4 = 5b - 10 }}}
(1) {{{ -2a + 5b = 6 }}}
and
(2) {{{ 2a + 20 = 3*( b + 10 ) }}}
(2) {{{ 2a + 20 = 3b + 30 }}}
(2) {{{ 2a - 3b = 10 }}}
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Add (1) and (2)
(1) {{{ -2a + 5b = 6 }}}
(2) {{{ 2a - 3b = 10 }}}
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{{{ 2b = 16 }}}
{{{ b = 8 }}}
and
(2) {{{ 2a - 3b = 10 }}}
(2) {{{ 2a - 3*8 = 10 }}}
(2) {{{ 2a = 24 + 10 }}}
(2) {{{ 2a = 34 }}}
(2) {{{ a = 17 }}}
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Jose is 17
Maria is 8
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check:
(1) {{{ a - 2 = (5/2)*( b - 2 ) }}}
(1) {{{ 17 - 2 = (5/2)*( 8 - 2 ) }}}
(1) {{{ 15 = (5/2)*6 }}}
(1) {{{ 15 = 5*3 }}}
(1) {{{ 15 = 15 }}}
OK
You can check (2)