Question

an item has increased 15%. a person can buy the item for a 25% employee discount. The employee pays 172.50. What was the price last year?

Answer 1

The employee bought it for 172.50, that's with a 25% discount, so 100% - 25% = 75%, so, the employee is only paying 75% of the current price, which is 172.50, let's say "x" is the regular price.

so, if "x" is the 100%, and we know that 172.50 is the 75%, what the dickens is "x"?

$\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 172.50&75 \end{array}\implies \cfrac{x}{172.50}=\cfrac{100}{75}\implies x=\cfrac{172.50\cdot 100}{75} \\\\\\ x=230$

now, we know the 230 is the price, but already increased by 15%, so hmm if say the item before the increase is say "p", which is 100%, and we know that 230 is 100% + 15% = 115%, then what is "p"?

$\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 230&115\\ p&100 \end{array}\implies \cfrac{230}{p}=\cfrac{115}{100}\implies \cfrac{230\cdot 100}{115}=p$