Question

Mary and dan went to a bookstore. mary bought 2 notebooks and 3 pens for $14.50. dan bought 1 notebook and 2 pens for $7.50. how much does one notebook cost?

Answer 1

Let
`n,p` be the cost, respectively, of a notebook and a pen. If you buy 2 notebooks and 3 pens (which we know is a cost of $14.50), you spend
`2n+3p`

Similarly, if you buy 1 notebook and 2 pens (which we know is a cost of $7.50), you spend
`n+2p`

These two equations form the following system:

`\begin{cases}2n+3p=14.5\\ n+2p=7.5 \end{cases}`

Multiply the second equation by 2:

`\begin{cases}2n+3p=14.5\\ 2n+4p=15 \end{cases}`

Subtract the first equation from the second:

`2n+4p - (2n+3p) = 15-14.5 \iff p=0.5`

So, a pen costs 0.5 dollars. Plug this equation in the second equation:

`n+2p=7.5 \iff n+2\cdot 0.5=7.5\iff n+1 = 7.5 \iff n=6.5`