SOLUTION: The price of milk is increased by 20%.Find by how much percent a housewife should reduce the consumption of milk so as to not to increase her expenditure?

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Question 918962: The price of milk is increased by 20%.Find by how much percent a housewife should reduce the consumption of milk so as to not to increase her expenditure?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = price per unit before going up
+p+%2B+.2p+=+1.2p+ = price per unit after going up
I can say they consumed any amount before
the price rose. I will say they consumed
+100+ units ( any units )
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Let +k+ = the fraction to reduce consumption by
+100p+=+%28+100+-+100k+%29%2A1.2p+
+100p+=+100%2A%28+1+-+k+%29%2A1.2p+
Divide both sides by +100p+
+1+=+1.2%2A%28+1+-+k+%29+
+1+=+1.2+-+1.2k+
+1.2k+=+.2+
+k+=+1%2F6+
She needs to reduce consumption by 16.67%
check:
Say +p+=+7+
+p+%2B+.2p+=+1.2%2A7+
+1.2%2A7+=+8.4+
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Say they consume +11+ units
+11%2A7+=+77+ is the cost of milk before increase
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Then they consume +11+-+%281%2F6%29%2A11+=+55%2F6+ units
after increase
+8.4%2A%2855%2F6%29+=+77+
Their cost still is the same after increase in price -OK