Pre-AP Record your answers on a sheet of paper.
Show your work.
11. Christine had one dress and three sweaters
cleaned at the dry cleaner and the charge
was $19.50. The next week, she had two
dresses and two sweaters cleaned for a
total charge of $23.00.
a. Let d represent the price of cleaning a
dress and s represent the price of
cleaning a sweater. Write a system of
linear equations to represent the prices
of cleaning each item.
b. Solve the system of equations using
substitution or elimination. Explain
your choice of method.
c. What will the charge be if Christine
takes two dresses and four sweaters
to be cleaned?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.