SOLUTION: when the price of a box of peanuts is increased by 30% its sales decreased by x% such that the revenue decreased by 9%.what is the value of x?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: when the price of a box of peanuts is increased by 30% its sales decreased by x% such that the revenue decreased by 9%.what is the value of x?       Log On


   

Question 864679: when the price of a box of peanuts is increased by 30% its sales decreased by x% such that the revenue decreased by 9%.what is the value of x?
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Idea applied is Price%2AItemCount=Revenue.
Let p = original price
Let q = original count of items sold
x/100 = the fraction of q not sold, compared to q.

Price____________Item Count__________Revenue
p________________q___________________pq
p(1.30)__________q-q%28x%2F100%29__________p%281.30%29%28q-q%28x%2F100%29%29=pq%281.30%29%281-x%2F100%29

Revenue decreased by 9% upon the price increase.
Also meaning, new revenue became 91% of original revenue, since 9+91=100.
highlight%28pq%281.30%29%281-x%2F100%29=pq%2891%2F100%29%29

1.30%281-x%2F100%29=91%2F100 Divided both members by pq.
1.3-%281.3%2F100%29x=91%2F100
130-1.3x=91
130-91=1.3x
1.3x=39
x=%283%2A13%29%2F%2813%2A0.1%29
highlight%28x=30%29
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The percent drop in count of items sold was 30.