Question

1. A vendor sells pretzels and drinks at a corner stand. He charges $2.25 for a pretzel and $1.50 for a drink. One day, the vendor made a total of $463.50 by selling a total of 257 items.

(a) Write a system of equations to represent the situation.
(b) How many pretzels and how many drinks did the vendor sell? Show your work.

Answer 1

a)
I:2.25*pretzels+1.5*drinks=463.50
II:pretzels+drinks=257

b)
with II:
pretzels+drinks=257
pretzels=257-drinks

substitute pretzels=257-drinks into I:
2.25*pretzels+1.5*drinks=463.50
2.25*(257-drinks)+1.5*drinks=463.50
2.25*257-2.25*drinks+1.5*drinks=463.50
-0.75*drinks=463.5-2.25*257
0.75*drinks=114.75
drinks=114.75/0.75=153

in II:
pretzels=257-drinks
pretzels=257-153=104