The history museum in Khiva sells two kinds of tickets: an adult ticket for 15 dollars and a student ticket for 9 dollars. On a busy Saturday in spring, the museum sold a total of 300 tickets, and the ticket office brought in 3,780 dollars.
On Monday the regional tourism office asked a simple question: how many of Saturday's visitors were students? The museum's ticket machine had broken that morning, and the cashier had written down only the two totals.
The museum director, Shohida, solved it without writing a single equation. Suppose, she said, that every one of the 300 visitors had been a student. Then the office would have taken 300 times 9, which is 2,700 dollars. But it actually took 3,780 dollars, which is 1,080 dollars more.
Each adult ticket costs 6 dollars more than a student ticket, so each adult adds 6 dollars to that imaginary total. To explain an extra 1,080 dollars, there must have been 1,080 divided by 6, or 180 adults. The other 120 visitors were students.
She checked the answer before sending it. One hundred and eighty adults at 15 dollars bring in 2,700 dollars, and 120 students at 9 dollars bring in 1,080 dollars. Together that is 3,780 dollars, and together they are 300 people. Both conditions were met.
The tourism office used the figure to plan a student discount week in the autumn. Shohida, meanwhile, asked for the ticket machine to be repaired and for the cashier to keep a separate tally of each kind of ticket. "Two totals can tell you two numbers," she said, "but only if you know how to ask them."