Two stationery shops compared

Statement

At shop A, $1$ euro buys $8$ pens or $12$ notebooks. At shop B, $1$ euro buys a bundle of $5$ pens and $5$ notebooks. Where is it cheaper to buy $300$ pens and $300$ notebooks?

Solution

Shop A. A pen costs $\dfrac{1}{8}$ euro and a notebook $\dfrac{1}{12}$ euro: $300\cdot\frac{1}{8} + 300\cdot\frac{1}{12} = 37.5 + 25 = 62.50\ \text{euro}.$ Shop B. Each bundle ($5$ pens $+\,5$ notebooks) costs $1$ euro; $60$ bundles are needed: $60\cdot 1 = 60.00\ \text{euro}.$ Shop B is cheaper, saving $2.50$ euro (that is $4\%$). $\boxed{\text{A}=62.50\ \text{euro},\quad \text{B}=60.00\ \text{euro}.}$