Question

A school trip to a museum cost $2,056. A total of 125 chaperones and students went on the trip. Adult admission to the museum costs $23, and student admission costs $16. How many chaperones and students went to the museum?

Answer 1

Answer:

Chaperones = 8 and Student = 117

Explanation:

Let,

Chaperones = x

Student = y

x + y = 125

=> x = 125 - y (1)

23x + 16y = 2056

=> 23(125 - y) + 16y = 2056

=> 2875 - 23y + 16y = 2056

=> 2875 - 7y = 2056

=> 2875 - 2056 = 7y

=> 819 = 7y

=> 819/7 = y

=> 117 = y

From 1

=> x = 125 - 117

=> x = 8

Answer 2

117 students, 8 adults

Explanation:

Let's say a adults went and s students went.

Total cost for adults = 23 for each a = 23a

Total cost for each student = 16s

Number of adults and students = a + s = 125

Total cost = 23a + 16s = 2056

a + s = 125

23a + 16s = 2056

We can solve this by solving for a and then plugging that into the other equation, making it so that there is only one variable

subtract s from both sides in the first equation

a = 125 - s

plug that into the second equation

23(125 - s) + 16s = 2056

2875 - 23s + 16s = 2056

2875 - 7s = 2056

subtract 2875 from both sides to isolate s and its coefficient

-7s = -819

divide both sides by -7 to isolate s

s = 117

a = 125 - s = 125 - 117 = 8