Question 1133494
Let {{{ a }}} = Jose's age now
Let {{{ b }}} = Edwin's age now
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For some reason, I like to this particular type
of problem from the end to the beginning.
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" when Edwin was half the age he will be ten years from now."
In {{{ 10 }}} yrs, Edwin will be {{{ b + 10 }}}
Half of that is {{{ ( b + 10 )/2 }}}
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" Edwin is as old as Jose was . . ."
I'll assume that Jose' is the older one
(1) {{{ b = ( b + 10 )/2 + ( a - b ) }}}
I put in the {{{ a - b }}} because the difference in their ages
never changes
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" when Jose's age was half the sum of their present ages. "
{{{ ( a + b )/2 }}}
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" when Jose is twice as old as Edwin was. . . "
Edwin was:
{{{ ( a + b )/2 - ( a - b ) }}}
" when Jose is "
{{{ 2*( ( a + b )/2 - ( a - b ) ) }}}
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" Jose is old as Edwin will be . . "
(2) {{{ a = 2*( ( a+ b )/ 2 - ( a - b ) ) - ( a - b ) }}}
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I have 2 equations with 2 unknowns, so it's solvable
(2) {{{ a = a + b - 2*( a - b ) - ( a - b ) }}}
(2) {{{ a = a + b - 2a + 2b - a + b }}}
(2) {{{ a = 4b - 2a }}}
(2) {{{ 3a = 4b }}}
(2) {{{ b = (3/4)*a }}}
and
(1) {{{ b = ( b + 10 )/2 + ( a - b ) }}}
(1) {{{ 2b = b + 10 + 2*( a - b ) }}}
(1) {{{ 2b = b + 10 + 2a - 2b }}}
(1) {{{ 2b = 2a - b + 10 }}}
(1) {{{ 3b = 2a + 10 }}}
Substitute (2) into (1)
(1) {{{ 3*(3/4)*a = 2a + 10 }}}
(1) {{{ 9a = 8a + 40 }}}
(1) {{{ a = 40 }}}
Jose' is 40 yrs old
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check:
(2) {{{ b = (3/4)*a }}}
(2) {{{ b = (3/4)*40 }}}
(2) {{{ b = 30 }}}
" when Edwin was half the age he will be ten years from now."
Edwin was {{{ ( 30 + 10 )/2 = 20 }}} yrs old
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" Edwin is as old as Jose was . . ."
(1) {{{ b = ( b + 10 )/2 + ( a - b ) }}}
(1) {{{ 30 = 20 + ( 40 - 30 ) }}}
(1) {{{ 30 = 20 + 10 }}}
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" when Jose's age was half the sum of their present ages. "
{{{ ( 40 + 30 )/2 = 35 }}}
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" when Jose is twice as old as Edwin was. . . "
Edwin was:
{{{ ( a + b )/2 - ( a - b ) }}}
{{{ 35 - ( 40 - 30 ) = 25 }}}
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" when Jose is "
{{{ 2*( ( a + b )/2 - ( a - b ) ) }}}
{{{ 2*25 = 50 }}}
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" Jose is old as Edwin will be . . "
(2) {{{ a = 2*( ( a+ b )/ 2 - ( a - b ) ) - ( a - b ) }}}
(2) {{{ 40 = 50 - ( 40 - 30 ) }}}
(2) {{{ 40 = 50 - 10 }}}
OK
Seems to check out. Get another opinion if needed