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The original selling price of a share of stock was d dollars. The selling price for a share of the same stock at a later date was represented by the expression 1.4(0.55 d). Which description could explain what happened to the price of the share of stock? The price decreased by 55% and then increased by 140% The price increased by 40% and then decreased by 45% The price decreased by 0.45% and then increased by 140% The price decreased by 0.55% and then increased by 0.4%

The original selling price of a share of stock was d d dollars. The selling price for a share of the same stock at a later date was represented by the expression 1.4(0.55d) 1.4(0.55 d) . Which description could explain what happened to the price of the share of stock?\newlineThe price decreased by 55% 55 \% and then increased by 140% 140 \% \newlineThe price increased by 40% 40 \% and then decreased by 45% 45 \% \newlineThe price decreased by 0.45% 0.45 \% and then increased by 140% 140 \% \newlineThe price decreased by 0.55% 0.55 \% and then increased by 0.4% 0.4 \%

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Q. The original selling price of a share of stock was d d dollars. The selling price for a share of the same stock at a later date was represented by the expression 1.4(0.55d) 1.4(0.55 d) . Which description could explain what happened to the price of the share of stock?\newlineThe price decreased by 55% 55 \% and then increased by 140% 140 \% \newlineThe price increased by 40% 40 \% and then decreased by 45% 45 \% \newlineThe price decreased by 0.45% 0.45 \% and then increased by 140% 140 \% \newlineThe price decreased by 0.55% 0.55 \% and then increased by 0.4% 0.4 \%
  1. Understand Expression: Understand the expression 1.4(0.55d)1.4(0.55d). The expression 1.4(0.55d)1.4(0.55d) can be broken down into two parts: 0.55d0.55d and 1.41.4. The 0.55d0.55d represents a 55%55\% decrease of the original price dd, because 0.550.55 is the same as 55100\frac{55}{100} or 55%55\%. The 1.41.4 represents a 1.4(0.55d)1.4(0.55d)11 increase of the price after the decrease, because 1.41.4 is the same as 1.4(0.55d)1.4(0.55d)33 or 1.4(0.55d)1.4(0.55d)44, which means the new price is 1.4(0.55d)1.4(0.55d)11 more than the price after the decrease.
  2. Calculate New Price: Calculate the new price after the initial decrease.\newlineTo find the new price after a 55%55\% decrease, we multiply the original price dd by 0.550.55. This gives us the price after the decrease.\newlineNew price after decrease = 0.55d0.55d
  3. Calculate Final Price: Calculate the final price after the subsequent increase.\newlineTo find the final price after a 40%40\% increase of the decreased price, we multiply the new price after decrease by 1.41.4.\newlineFinal price = 1.4×(0.55d)1.4 \times (0.55d)
  4. Interpret Price Change: Interpret the expression in terms of the price change.\newlineThe expression 1.4(0.55d)1.4(0.55d) represents a two-step price change. First, the price decreases by 55%55\%, and then the decreased price is increased by 40%40\%. This is the correct interpretation of the expression.

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