Chocolate Machine

He makes $8-$3=$5 per chocolate bar, so he has to sell $400/$5=80 chocolate bars to not be at a loss of money.

For each chocolate bar he sells for $8, he is at a $3 loss due to manufacturing costs. So he gains 8-3 = $5 per chocolate bar. TO regain the money he spent on the machine(which was $400), he needs to sell 400/5 = 80 chocolate bars.

This is a simple way of thinking about marketing and business

Let's make a variable ( $m$ ) and set it to $0$ (his beginning money). Because the chocolate-making machine costs $\$400$ , $m =-400$ . He gets $\$8$ for selling one bar but needs $\$3$ to make that bar so his profit is $\frac{\$8-\$3=\$5}{bar}$ . We can see that the profit and the number of bars have a $5:1$ correspondence. Because $m=-400$ , We crank the profit up to $400$ (to set $m$ to a non-negative number(so he doesn't lose any money overall)). Since the profit and the number of bars have a $5:1$ correspondence, the answer is $400:400÷5=\boxed{80}$

He has a profit of 8-3=5$ per chocolate bar. 400/5=80 chocolate bars to be not t at loss of money.

For every chocolate he earns a profit of $5 ($8-$3).

As he had invested $400 for machine, he would need to sell $400/$5 chocolates

i.e 80 chocolates

Let $n$ be the number of chocolate {he makes or sells}

We know that initially, he pays $\boxed{ \$400}$

$\therefore400 + 3n > 8n \\ 400 > 5n \\ \color{#3D99F6} n < \boxed{ 80 }$