Chapter 7, Problem 30CP

To determine

The buying price of card given its current value as a percentage of the price and an offered amount as a certain proportion of the present value

Answer to Problem 30CP

Will paid $\$22.5$ for the card.

Explanation of Solution

Given Information:

• Present value is $80\%$ more than the price of the card
• The offered amount of $27\$$ is only $\frac{2}{3}$ of the value of the card

Method: Write the present value in terms of the price of the card. The equate $\frac{2}{3}$ times the present value of the card to the offered amount.

If the price of the card is $p$ , then the present value of the card is $p+80\%\cdot p$ .

So, present value is

  $p+80\%\cdot p=p+0.8p=1.8\times p$

  $\frac{2}{3}$ of the current price is

  $\frac{2}{3}\times 1.8\times p=\frac{3.6\times p}{3} = 1.2p$

Equate the above obtained expression for $\frac{2}{3}$ of the current price to the offered price to write

  $1.2p = \$27$

Divide the equation by $1.2$ to get

  $p=\frac{27}{1.2}=\$22.5$