SOLUTION: grace bought 10 handkerchief and 8 fans for 312.00 pesos. after a week, at the same prices, she bought 12 handkerchief and 5 fans for 264.oo pesos. find the cost of each item.

Question 669184: grace bought 10 handkerchief and 8 fans for 312.00 pesos. after a week, at the same prices, she bought 12 handkerchief and 5 fans for 264.oo pesos. find the cost of each item.
Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
Establish variables
x = handkerchief
y = fan
...
10x + 8y = 312
12x + 5y = 264
...
Multiply the first equation by -5 and the second one by 8
-5(10x+8y=312)
8(12x+5y=264)
yielding
-50x + -40y = -1560
96x + 40y = 2112
Add
-50x + 96x + -40y + 40y = -1560 + 2112
46x = 552
dollar handkerchief
...
Multiply the first equation by 12 and the second one by -10
12(10x+8y=312)
-10(12x+5y=264)
yielding
120x + 96y = 3744
-120x + -50y = -2640
Add
120x + -120x + 96y + -50y = 3744 + -2640
46y = 1104
dollar fan
.....................
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