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HELP DUE ON FRIDAY!!!!MATH!!!!!!?
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?
2 Answers
- Jun AgrudaLv 71 decade agoFavorite 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.
