# Shoes offer

Carmen and Jorge have gone together to buy some shoes and have taken advantage of a 2 x 1 occasion. The shoes that Carmen has chosen were marked with the price of 20 euros and Jorge's were 35.

As usual in these cases, they have had to pay only 35 euros (the price of the most expensive) for taking the two pairs. The fact is that now they do not know very well how to determine the amount that corresponds to each one.

How much should each one pay to distribute the savings as fairly as possible?

#### Solution

Since each one separately would have spent a different amount on his pair of shoes, the money saved should be distributed in proportion to what they were going to spend.

Carmen has taken a product of 20 while Jorge has taken one of 35, that is, for every 20 euros worth of the pair of Carmen, Jorge takes 35, or a ratio of 4 to 7.

That means that for every 11 euros they pay, Jorge should pay 7 and Carmen 4. Since they have paid between the two 35, dividing this amount by 11, give 3 with just over 18 cents for what Carmen should pay 3.1818 * 4 = 12.73 (rounding) and Jorge 3.1818 * 7 = 22.27 which makes a total of 35 euros.

Looking at what they have saved, Jorge will have saved 12.73 and Carmen 7.27 which in both cases corresponds to a percentage of savings of 36.36%.