Answer:
a pair of Tap shoes costs $169.50
a pair of Point shoes costs $319.00
a pair of Ballet shoes costs $159.50
Explanation:
first tell your teacher, that the problem description is misleading.
as a shoe store has more than one pair per type. so, "all the shoes" would mean all the sites in the store. but that is for sure not meant here.
what your teacher hopefully meant was that the total price of buying one pair of each of the shoe types is $648.
and your teacher was hopefully asking for the price of pairs of shoes, and not actually single shoes.
my solution bases on these assumptions.
so, we got Tap (t), Point (p) and Ballet (b) shoes.
buying one pair each is
t + p + b = 648
now we know some other information.
p = 2×b (Point shoes are double the price of Ballet shoes)
t = b + 10 (Tap $10 more than Ballet)
so, we can replace t and p by expressions of b and get
b + 10 + 2×b + b = 648
4×b + 10 = 648
4×b = 638
b = 159.50
p = 2×159.50 = 319.00
t = 159.50 + 10 = 169.50