HELP DUE ON FRIDAY!!!!MATHS!!!!!!?

Question

Three fashion conscious young women were downtown shopping one day when they saw a hat that they all liked, priced at $170. The each checked their purses.
1.The first said to the other two: "If you lend me half of what you have I can but the hat!"
2. The second said to the other two: "If you lend me one-third of what you have, I could buy the hat!
But, said the third lady, "If you both lend me one quarter of what you have I could buy the hat!"

How much did they each have in their purses?
Don't just give an answer, show working please.
This is urgent!

Jun Agruda · Accepted Answer

Money of 1st lady (x):
x + 1/2y + 1/2z = $170
x = $170 - 1/2y - 1/2z

Money of 2nd lady (y):
y + 1/3($170 - 1/2y - 1/2z) + 1/3z = $170
y + $170/3 - 1/6y - 1/6z + 1/3z = $170
6/6y - 1/6y = $510/3 - $170/3 + 1/6z - 2/6z
5/6y = $340/3 - 1/6z
y = $136 - 1/5z

Money of 1st lady (x):
= $170 - 1/2($136 - 1/5z) - 1/2z
= $170 - $68 + 1/10z - 5/10z
= $102 - 2/5z

Money of 3rd lady (z):
z + 1/4($102 - 2/5z) + 1/4($136 - 1/5z) = $170
z + $25.50 - 2/20z + $34 - 1/20z = $170
17/20z = $110.50
z = 130

Money of 1st lady:
= $102 - 2/5($130)
= $102 - $52
= $50

Money of 2nd lady:
= $136 - 1/5($130)
= $136 - $26
= $110

Answer: $50, $110 & 130 are what the 1st, 2nd & 3rd ladies have, respectively.

William B · Answer

first =x, second =y, third =z
x +1/2(y +z) =170
2x +y +z =340

y +1/3(x+z) =170
3y +x +z =510

z +1/4(x+z) =170
4z +x+y =680
Subtracting second equation from the third gives 3z -2y =170

Subtracting twice second equation from the first gives  -z -5y =-680
-17y =-1870
y=110
-z -5(110) =-680
-z = -130
z=130
4(130) +x +110 =680
520 +110 +x =680
630 +x=680
x=50
first has $50
second has $110
third has $130

S.Gomez · Answer

sucks to be you...

do your own homework.

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HELP DUE ON FRIDAY!!!!MATHS!!!!!!?

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