   SEARCH HOME Math Central Quandaries & Queries  Question from Margaret: What is the formula to find the 75% off full price item that was already marked 30% off? Hi Margaret,

I'm not sure what you need. Do you know the original price? Do you know the 30% off price?

Do you want to find the price if the 30% off price is reduced by 75% or do you want to know the what the price would be original price were reduced by 75%? Perhaps you want something else.

Penny

Margaret wrote back

Penny,Thank you for your response. I work retail. Our employee discount is 75%. If there is an item that's on sale we can't override the price so I have to figure out what that item would be to give the 75% off price.

An example,

An item is $\$100,$it's marked down 30% or$\$70,$ the employee discount would be 75% of $\$100$for a total of$\$25.$ Is there a formula I can use to come up the correct price? I know the end number but have to do this with percentages.

Margaret

Thanks Margaret. I understand now.

Suppose the original price of the item is $\$p,$in your example$\$p = \$100,$and the sale price is$\$s,$ in your example $\$s = \$70.$ Suppose also that the employee price is $\$e,$in your example$\$e = \$25.$You know$\$s$ and you want to determine $\$p$so that you can calculate$\$e.$

Since the sale is 30% off the relationship between $\$p$and$\$s$ is that $\$s$is 70% of$\$p$ or

$s = 0.70 \times p.$

Thus

$p = \frac{s}{0.70}.$

Since employees get a 75% discount, $\$e$is 25% of$\$p,$ and hence

$e = 0.25 \times p.$

Putting the two expressions together gives

$e = 0.25 \times \frac{s}{0.70} = \frac{0.25}{0.70} \times p = \frac{25}{70} \times p$

which simplifies to

$e = \frac{5}{14} \times p.$

I hope this is what you are looking for.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.