Question 179541
Let {{{m}}}= the Mother's age now
Let {{{s}}}= her Son's age now
In 4 years, the Mother's age will be {{{m + 4}}}
In 4 years, the Son age will be {{{s + 4}}}
4 years ago, the Mother's age was {{{m - 4}}}
4 years ago, the Son's age was {{{s - 4}}}
given:
(1) {{{m + 4 = 3*(s + 4)}}}
(2) {{{m - 4 = 5*(s - 4)}}}
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There are 2 equations and 2 unknowns, so it's solvable
(1) {{{m + 4 = 3s + 12}}}
(2) {{{m - 4 = 5s - 20}}}
Now subtract (1) from (2)
(2) {{{m - 4 = 5s - 20}}}
(1) {{{-m - 4 = -3s - 12}}}
{{{-8 = 2s - 32}}}
{{{2s = 24}}}
{{{s = 12}}}
Substitute this in (2)
(2) {{{m - 4 = 5*12 - 20}}}
{{{m - 4 = 60 - 20}}}
{{{m - 4 = 40}}}
{{{m = 44}}}
The Mother is 44 and the Son is 12
check:
(1) {{{m + 4 = 3*(s + 4)}}}
(1) {{{44 + 4 = 3*(12 + 4)}}}
{{{48 = 48}}}
(2) {{{m - 4 = 5*(s - 4)}}}
(2) {{{44 - 4 = 5*(12 - 4)}}}
{{{40 = 40}}}
OK