Question

Michael bought 8 new Pokemon cards to add to his collection.The next day his dog ate half of his collection. There are now only 40 cards left. How many cards did Michael start with? Write out equation and solve. Show work

Answer 1

Let x be the initial amount of cards that Michael had.

Since he bought 8 new Pokémon cards, the total number of cards that he had at that moment was x+8.

After his dog ate half the amount of cards that Michael had, the number of cards was reduced to:

`(x+8)/(2)`

Since he has 40 cards left, then:

`(x+8)/(2)=40`

Solve for x to find the amount of cards that Michael had at the beginning. Multiply both members by 2:

`\begin{gathered} 2*(x+8)/(2)=2*40 \\ \Rightarrow x+8=80 \end{gathered}`

Substract 8 from both members of the equation:

`\begin{gathered} x+8-8=80-8 \\ \Rightarrow x=72 \end{gathered}`

Therefore, the amount of cards Michael started with, was:

`72`