Question

The value of an autographed baseball card increased from $39 to $65. What is the percent increase in value of the baseball card? Round to the nearest hundredth of a percent

Answer 1

The percent increase in value of the baseball card is 66.667%

Explanation:

You must first determine the amount of money increased by the value of an autographed baseball card. For this you must subtract the price with the applied increase and the original price of the card: $65-$39=$26

This will be the amount of increase. Then, one way to calculate the percentage increase in the value of the baseball card is through a direct rule of three.

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three. Remember that proportionality is a constant relationship or ratio between different magnitudes.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (Or when one magnitude decreases, so does the other), the direct rule of three must be applied. To solve a direct rule of three, the following formula must be followed:

a ⇒ b

c ⇒ x

Then

`x=(c*b)/(a)`

In this case, the rule of three applies as follows: If the original price ($ 39) represents 100%, what is the value of the percentage in the value of the baseball card when its value increases $ 26?

`percentage=(26*100)/(39)`

percentage=66.667%

Another way of thinking about it is considering that:

change from the original price = percentage of change*original price

In this case: $26=percentage of change*$39

So, isolating the percentage of change you get:

`percentage of change=(26)/(39) =0.66667`

This value is expressed in decimal, and for it to be expressed in fraction you must multiply it by 100 (100%). Then you get:

percentage of change=0.66667*100%

percentage of change=66.667%

Note that the value obtained is the same as in the previous case, so both ways of thinking the solution to this problem is correct

Finally, the percent increase in value of the baseball card is 66.667%

Answer 2

The percent increase is found by finding the difference between the two prices and then dividing that different by the beginning price.

For this example it would be 65-39= $26. So $26/$39(the starting price) is 0.666... This is equivalent to about 66.67%. So, the price of the card increased by about 66.67%