At first, Felicia has 7 units of money.

1/7 of her money ie 1 unit of money is spent. This leaves behind 6 units of money.

She then spent 2/3 of her remaining 6 units of money ie 4 units of money on more badges.

Now she has 2 units of money left, which is 2/7 of her starting money.



Since 1 keychain cost 4 times as much as 1 badge, buying 6 keychains is as good in money as buying 24 badges. So buying 6 keychains and 13 badges is the same in price as buying 37 badges.

So she uses 1 unit of her money to buy “37 badges”.

4 units
= 37 x 4
= 148

so she bought 148 more badges. In actual fact, she bought only 13 badges.

So, total number of badges
= 148 + 13
= 161