fambrini wrote:The price of a left-handed widget increased 20% in 1981 and 10% in 1982. By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price?
A) 40%
B) 35%
C) 30%
D) 26%
E) 24%
OA: E
We can let the pre-1981 price of the widget = x.
Thus, after a 20% increase in price, in 1981, the new price is 1.2x.
After a 10% increase in price, in 1982, the new price is 1.1(1.2x) = 1.32x.
We need to determine by approximately what percentage would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price. We can create the following equation in which n = the percentage decrease.
(1.32x)(1 - n/100) = x
(1.32x)[(100-n)/100] = x
We can convert 1.32 to a fraction and cancel out the x's, so we have:
(132/100)[(100-n)/100] = 1
(100-n)/100 = 100/132
Cross-multiplying gives us:
132(100 - n) = 10,000
13,200 - 132n = 10,000
132n = 3200
n = 3200/132 ≈ 24
Answer:
E
