Elementary Algebra Question

Question

A man has distributed his baseball card collection evenly on shelves, putting 33 cards on each shelf. If he adds 2 shelves and redistributes his collection evenly on all the shelves, each shelf will have 27 cards. How many cards are in his collection?

Answer 1

We can denote the amount of shelves with the variable s.

So, at first, the man distributed his cards among s shelves. And each shelf contained 33 cards. Multiply the amount of cards per shelf by the amount of shelves to get the total card collection.

We can write this as 33s. Or, 33 • s.

After he rearranges the cards he has 27 cards in each shelf but also has 2 more shelves than previously. We can say then that now there are s + 2 shelves. Multiply the amount of cards per shelf by the amount of shelves to get the total card collection.

We can write this as 27(s + 2). Or, 27 • (s + 2).

The total amount of cards in the collection remains the same despite the rearrangement. So, we can say the 33s is equal to 27(s + 2).

Write it as 33s = 27(s + 2).

Solve the equation for s

33s = 27(s + 2)

33s = 27s + 54

6s = 54

s = 9

Now that we've solved for s, we can plug it back into either of the expressions to find the total card collection.

33(9) = 297