Question

The general admission fee to a museum is $20 for an adult. The admission fee is reduces by %40 for a student. A total of $860 was collected from 55 museum visitors in one day. Find the number of adults and students who visited the museum.

Answer 1

25 adults and 30 students

Explanation:

Let x be the number of adults and y be the number of students that visited the museum in one day. Then

`x+y=55.`

x adults pay $20x and y students pay $20·0.6·y (because the the admission fee was reduced by 40%, then the admissin fee bacame $20·(1-0.4)=$20·0.6 ).

Thus,

`20x+20\cdot 0.6\cdot y=860.`

Therefore, you have to solve the system of two equations:

`\left{\begin{array}{l}x+y=55\\20x+20\cdot 0.6\cdot y=860\end{array}\right.`

From the first equation
`x=55-y,` substitute it into the second one:

`20(55-y)+20\cdot 0.6\cdot y=860,\\ \\1100-20y+12y=860,\\ \\-20y+12y=860-1100,\\ \\-8y=-240,\\ \\y=(-240):(-8),\\ \\y=30`

and

`x=55-30=25.`