Question

A store sells small notebooks for ​$7 and large notebooks for ​$14. If a student buys 6 notebooks and spends ​$63​, how many of each size did he​ buy?

Answer 1

let the student bought x small notebooks
and y large notebooks
ATQ

x+y=6. .........(1)

Also,
7x+14y=63.......(2)

solving 1 and 2 for x and y we get
7x+7y=42
7x+14y=63
on subtracting
7y=21
y=3

He bought 3 small notebooks and 3 large notebooks

Answer 2

Given:

    Small notebooks = $7

     Large notebooks = $14

Answer:

     It is a known fact that 63 is a multiple of 7.

In fact, 7 * 9 = 63

We could assume that the student just bought 9 small notebooks, but this answer may be invalid as the student could have also bought few large notebooks.

So, the best way to figure out this problem would be to assume maximum number of large books and fill up the remaining slots with small books.

For example,

               If the student had bought, say four large notebooks, the amount spent would be $14 * 4 which would total up to $56, which leaves $7 remaining, so we could say that 1 small notebook was bought. But in this case, the total number of books only add up to 5, which leads to the conclusion that this assumption was incorrect.

                So lets reduce it down a bit and assume that 3 large notebooks were bought. In this case, the cost would add up to $42, which leaves $21 remaining. So in this case, 3 small notebooks can be bought, which adds up to the total of 6 books.

To summarize,

    ⇒ Number of small notebooks = 3

    ⇒ Number of large notebooks = 3