Question

8.3.9 On December 1, Tom's House of Dollhouses increased the prices on all of its dolls by 25%. In January, Tom is having a sale where all dolls are priced 20% off the December prices. For any doll, is the January price higher than, lower than, or the same as the November price for that same doll? Does your answer depend on the doll's original price?

Answer 1

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Answer 2

Answer:

The January price of the doll is same as the November price. It does not depend on the original price.

Step-by-step explanation:

- We are given with a word problem

- We are asked to find whether the January price is higher or lower or equal to the November price.

- We can do this in two steps

Step 1 : Finding the price of doll in December and January

Step 2 : Comparing them.

Step 1 of 2

Let x be the price of any doll in Tom's House.

The percentage increase in December is 25%

That is $\frac{1}{4} \times x=\frac{x}{4}$

Then the price in December is

$x+\frac{x}{4}=\frac{4 x+x}{4} \\ \frac{4 x+x}{4}=\frac{5 x}{4}$

And the percentage decrease in January is 20%

That is $\frac{20}{100}=\frac{1}{5}$ of that price in December

$\begin{aligned}\frac{1}{5} \times \frac{5 x}{4} &=\frac{5 x}{5 \times 4} \\\frac{5 x}{20} &=\frac{x}{4}\end{aligned}$