Santiago is working at his mom’s day care this summer. His mom has asked him to check out the

Question

library book sale to look for books they might be able to use in the day care. When he gets to the
book sale, he sees that board books are $1.50 and soft cover books are $0.50. He picks out a
variety of books and spends $20.
Suppose Santiago bought 34 books. Can you figure out how many of each type of book he
bought?

Answer 1

Let's denote the number of board books Santiago bought as \( x \) and the number of soft cover books as \( y \). We are given two pieces of information:

1. The total number of books Santiago bought is 34: \[ x + y = 34 \]

2. The total cost of the books is $20, with board books costing $1.50 and soft cover books costing $0.50: \[ 1.5x + 0.5y = 20 \]

Now we have a system of two equations:

1. \( x + y = 34 \)
2. \( 1.5x + 0.5y = 20 \)

We can simplify the second equation by multiplying it by 2 to eliminate the decimal: \[ 3x + y = 40 \]

Now we have the new system of equations:

1. \( x + y = 34 \) (1)
2. \( 3x + y = 40 \) (2)

Next, we can solve this system. We can subtract equation (1) from equation (2): \[ (3x + y) - (x + y) = 40 - 34 \]

This simplifies to: \[ 2x = 6 \]

Dividing both sides by 2 gives: \[ x = 3 \]

Now we can substitute \( x = 3 \) back into equation (1): \[ 3 + y = 34 \] \[ y = 34 - 3 = 31 \]

So, Santiago bought:

• 3 board books and
• 31 soft cover books.

To verify, we can check both conditions:

• Total number of books: \[ 3 + 31 = 34 \quad \text{(Correct)} \]

• Total cost: \[ 1.5(3) + 0.5(31) = 4.5 + 15.5 = 20 \quad \text{(Correct)} \]

Thus, the solution is that Santiago bought 3 board books and 31 soft cover books.