Equation: Apple problem I'm stuck with a question from school, not even the teacher knew this one: **Question:** Ben goes to the market and pays \$12 for apples (amount unknown), but they were so small that the cashier gave Ben two apples for free. In this way, the price for a dozen apples dropped by exactly \$1. How many apples did Ben get for \$12?

Let's define

$p$ \- regular prize of the apples per apple

$p^*$ \- reduced prize of the apples per apple

$n$ \- number of apples originally bought

Then we have the following equations:

$n\cdot p=12$ \- he payed 12 dollars

$(n+2)\cdot p^*=12$ \- he payed 12 dollars for two more apples with the fictional reduced prize

$p\cdot 12 = p^*\cdot12+1$ \- the price for a dozen apples is reduced by 1

Solving these equations leads to a quadatric equation which has two possible solutions $n=16$ or $n = -18$.

Please feel free to comment if you like to see the way to actually solve the equations not just the set up.