SOLUTION: the price of an item was increased by 10%. this reduced the monthly sales by 20%. find the overall effect on the value of monthly sale

Question 1072149: the price of an item was increased by 10%. this reduced the monthly sales by 20%. find the overall effect on the value of monthly sale
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
price was raised by 10%.

monthly sales were reduced by 20%.

let x = the original price of each item.
let y = the original number of units sold.

the value of the original sales is equal to x * y

the price is raised 10% to become x + .10 * x = 1.1 * x.

the number of units sold is decreased by 20% to become y - .20 * y = .8 * y

the total revenue now becomes 1.1 * x * .8 * y.

simplify to get total revenue now becomes .88 * x * y

.88 * x * y / (x * y) = .88 = 88%.

the effect on the value of the monthly sales is that they are now equal to 88% of what they once were.

that's a reduction in the value of the monthly sales of 12%.

this is easier to see with numbers.

assume the price was 100 dollars per unit and that you sold 100 units each month.

the value of the monthly sales would be 100 * 100 = $10,000 monthly.

the price goes up 10% to become $110 per item.

the monthly units sold goes down 20% to become 80.

the monthly revenue is now 110 * 80 = $8,800 monthly.

the difference is $10,000 - $8,800 = $1,200.

the percent drop in income is $1,200 / $10,000 = .12 = 12%.

the value of the new monthly sales divided by the value of the old monthly sales is 8,800 / 10,000 = .88 = 88%.

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