Question 859986
Let their ages today be {{{ a }}} and {{{ b }}} days 
Let {{{ a }}} be the older kitten
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Yesterday their ages were {{{ a - 1 }}} days
and {{{ b - 1 }}} days
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(1) {{{ a - 1 = 4*( b - 1 ) }}}
(2) {{{ a + b = 10 }}}
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(1) {{{ a - 1 = 4b - 4 }}}
(1) {{{ -a + 4b = 3 }}}
Add equations (1) and (2)
(1) {{{ -a + 4b = 3 }}}
(2) {{{ a + b = 10 }}}
{{{ 5b = 13 }}}
{{{ b = 13/5 }}}
and
(2) {{{ a + 13/5 = 10 }}}
(2) {{{ a = 50/5 - 13/5 }}}
(2) {{{ a = 37/5 }}}
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Their ages are 7.4 days and 2.6 days
check:
(1) {{{ a - 1 = 4*( b - 1 ) }}}
(1) {{{ 37/5 - 1 = 4*( 13/5 - 1 ) }}}
(1) {{{ 32/5 = 4*( 8/5 ) }}}
(1) {{{ 32/5 = 32/5 }}}
OK