Question 1045351
joanne and alex had some money.
joanne gave 1/4 of her money to her mom.
j = original amt: She has {{{3/4}}}j now
she then saved and spent the rest in the ratio of 1:2.
That means she saved {{{1/3}}}*{{{3/4}}}j = {{{3/12}}}j = {{{1/4}}}j saved
That means she spent {{{2/3}}}*{{{3/4}}}j = {{{6/12}}}j = {{{1/2}}}j spent
:
alex spent one sixth on clothes and one third on books.
he saved the rest.
a = Alex's original amt: He has a - {{{1/6}}}a - {{{1/3}}}a =  {{{3/6}}}a = {{{1/2}}}a remains (saved)
:
The amount joanne gave her mom was equal to the amount alex spent on books.
{{{1/4}}}j = {{{1/3}}}a
multiply both sides by 12, get rid of the denominators
3j = 4a
solve for a
a = {{{3/4}}}j
:
 If joanne Then gave alex $180 from her savings she would only have one quarter of alexs savings.
{{{1/4}}}j - 180 = {{{1/4}}} * {{{1/2}}}a
{{{1/4}}}j - 180 = {{{1/8}}}a
multiply both sides by 8
2j - 1440 = a
2j = a + 1440
replace  a with {{{3/4}}}j
2j = {{{3/4}}}j + 1440
2j - {{{3/4}}}j = 1440
{{{8/4}}}j - {{{3/4}}}j = 1440
{{{5/4}}}j = 1440
j = 1440 * {{{4/5}}}
j = $1152
and 
a = {{{3/4}}}*1152
a = $864 
:
how much did they have initially: j had $1152; a had $864
:
how much did they spend together.
j spent {{{1/2}}} *1152 = $576
a spent {{{1/2}}} * 864 = $432
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Total amt spent together: $1008