Task 10/61 In a photo equipment store, a customer asks: "How much does this lens cost?" The saleswoman replies: "With leather case 115.00 DM, sir!" - "And how much does the lens cost without the case?" the customer asks further. "Exactly 100.00 DM more than the case!" says the saleswoman with a smile. How much does the lens cost?
If we denote the price of the lens by $x$ and the price of the case by $y$, then

$$
x+y=115 \quad ; \quad x-y=100
$$

(Both together cost 115 DM, the lens costs 100 DM more than the case.) Solving this system of equations, we get $x=107.50 \mathrm{DM} ; y=7.50 \mathrm{DM}$. Indeed, at these prices, the lens with the case costs 115.00 DM and the lens without the case costs 100.00 DM more than the case.