Question 971688: A woman buys 20 lemons at x cents and 30 oranges at y cents each. she packs them into bags which contain 4 lemons and 6 oranges and sells the bags at (5x+8y) cents each. find x,y if the amount of money on the fruit is $ 1.90 and the money she made by selling all the fruit is $ 2.50.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A woman buys 20 lemons at x cents and 30 oranges at y cents each.
she packs them into bags which contain 4 lemons and 6 oranges and sells the bags at (5x+8y) cents each find x,y if the amount of money on the fruit is $ 1.90 and the money she made by selling all the fruit is $ 2.50.
:
Find how many bags she sold, each bag has 4 lemons and 6 oranges
She has a total of 20 lemons and 30 oranges: 20/4 and 30/6; both = 5
She can sell 5 bags
Her total cost then: 5 * 1.90 = $9.50
;
She made 2.50, therefore her total from sales: 9.50 + 2.50 = $12.00
Find the selling price per bag: 12/5 = $2.40
:
Cost per bag equation: 4x + 6y = 1.90
Retail per bag equation: 5x + 8y = 2.40
use elimination here, multiply the 1st equation by 4, the 2nd equation by 3
16x + 24y = 7.60
15x + 24y = 7.20
-----------------Subtraction eliminates y, find x
x = .40 for the lemons
:
then using 5x + 8y = 2.40, find y
5(.40) + 8y = 2.40
2.00 + 8y = 2.40 - 2.00
8y = .40
y = .40/8
y = .05 for oranges, seems kind of low, but the figures all fit.
:
Let me know if I am right about this one. ankor@att.net
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