SOLUTION: Hi joanne and alex had some money.joanne gave 1/4 of her money to her mom.she then saved and spent the rest in the ratio of 1:2.alex spent one sixth on clothes and one third on bo

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Question 1045351: Hi
joanne and alex had some money.joanne gave 1/4 of her money to her mom.she then saved and spent the rest in the ratio of 1:2.alex spent one sixth on clothes and one third on books.he saved the rest. The amount joanne gave her mom was equal to the amount alex spent on books. If joanne
Then gave alex $180 from her savings she would only have one quarter of alexs savings.
how much did they have initially
how much did they spend together.
Thanks



Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
joanne and alex had some money.
joanne gave 1/4 of her money to her mom.
j = original amt: She has 3%2F4j now
she then saved and spent the rest in the ratio of 1:2.
That means she saved 1%2F3*3%2F4j = 3%2F12j = 1%2F4j saved
That means she spent 2%2F3*3%2F4j = 6%2F12j = 1%2F2j 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%2F6a - 1%2F3a = 3%2F6a = 1%2F2a remains (saved)
:
The amount joanne gave her mom was equal to the amount alex spent on books.
1%2F4j = 1%2F3a
multiply both sides by 12, get rid of the denominators
3j = 4a
solve for a
a = 3%2F4j
:
If joanne Then gave alex $180 from her savings she would only have one quarter of alexs savings.
1%2F4j - 180 = 1%2F4 * 1%2F2a
1%2F4j - 180 = 1%2F8a
multiply both sides by 8
2j - 1440 = a
2j = a + 1440
replace a with 3%2F4j
2j = 3%2F4j + 1440
2j - 3%2F4j = 1440
8%2F4j - 3%2F4j = 1440
5%2F4j = 1440
j = 1440 * 4%2F5
j = $1152
and
a = 3%2F4*1152
a = $864
:
how much did they have initially: j had $1152; a had $864
:
how much did they spend together.
j spent 1%2F2 *1152 = $576
a spent 1%2F2 * 864 = $432
--------------------------------
Total amt spent together: $1008