Question

Matilde spent two thirds of her money in one shop. She then spent two thirds of the remainder in a second shop. If she then had €18 left, how much money did she start out with?

Answer 1

Answer: Let's start by assuming that Matilde started out with some amount of money, which we will call "x" (in euros).

According to the problem, she spent two-thirds of her money in the first shop. This means that she had one-third of her money left after leaving the first shop:

Money left after first shop = x - (2/3)x = (1/3)x

Matilde then spent two-thirds of this remaining money in the second shop. This means that she had one-third of her original money left after leaving the second shop:

Money left after second shop = (1/3)x - (2/3)(1/3)x = (1/9)x

We are told that she had €18 left at this point so that we can set up an equation:

Money left after second shop = (1/9)x = 18

Solving for x, we get:

x = 162

Therefore, Matilde started out with €162.

Explanation: