  We consider a gravity theory coupled to matter, where the matter has a
higher-dimensional holographic dual. In such a theory, finding quantum extremal
surfaces becomes equivalent to finding the RT/HRT surfaces in the
higher-dimensional theory. Using this we compute the entropy of Hawking
radiation and argue that it follows the Page curve, as suggested by recent
computations of the entropy and entanglement wedges for old black holes. The
higher-dimensional geometry connects the radiation to the black hole interior
in the spirit of ER=EPR. The black hole interior then becomes part of the
entanglement wedge of the radiation. Inspired by this, we propose a new rule
for computing the entropy of quantum systems entangled with gravitational
systems which involves searching for "islands" in determining the entanglement
wedge.
