Question

Chris and Julia visit a book store. Chris buys three novels and four comic books for $36.75. Julia also buys three novels, but can only afford to buy one comic book. Her purchase cost is $32.25. What is the cost of a novel?

Answer 1

$10.25

Explanation:

A novel can be n, and comic book can be c.

If Chris buy 3 novels and 4 comic books, that's
`n+n+n+c+c+c+c`

or
`3n+4c`

So we know
`3n+4c=36.75`

If Julia buys 3 novels and 1 comic book, that's
`n+n+n+c`

or
`3n+c`

So we also know
`3n+c=32.25`

Now we can solve this as a simultaneous equation.

If we minus these two equations, the two
`3ns` cancel and we end up with
`3c=4.5`

This means
`c=1.5`, so one comic book is $1.50

If we substitute
`c` back into one of the equations,
`3n+4(1.50)=36.75`

Which is
`3n+6=36.75`

Add 6 to both sides of the equation and you get
`3n=36.75-6`, or
`3n=30.75`.

Divide 3 from each side and you get
`n=10.25`, so a novel costs $10.25