Question

"A local water park charges $18 per kid and $25 per adult for all-day admission. On its best day of the summer, the park sold 8 times as many kid tickets as adult tickets. The park brought in a staggering total of $58,056 in ticket sales that day."

A student used the following system of equations to model the situation given above. Which statement about the system of equations the student used is true?
{8a-k=0}
{20a+18k=58,056}
2003-11-04-00-00_files/i0310000.jpg
A.
The system of equations the student used is correct.
B.
The top equation in the system is incorrect.
C.
The bottom equation in the system is incorrect.
D.
Both equations in the system are incorrect.

Answer 1

there was no image it was a system glitch from pasting the answers (a,b,c,d)

Answer 2

can you explain as to why it wouldn't?

Answer 3

oh okay I understand. thank you so much

Answer 4

I almost forgot, welcome to QuestionCove cx

Answer 5

Thank you!

Answer 6

Why wouldn't \(8a-k=0\) work? Since \(a\) is the number of adult tickets sold and \(k\) is the number of kid tickets sold, the expression \(8a - k = 0 \iff k = 8a\) simply means that the park sold 8 times as many kid tickets as adult tickets.
I believe the top equation is correct.

Answer 7

Actually, I agree with @DuarteME . If you think about it, you have 8 times as many kid tickets in order to reach the number of adult tickets sold. So when equivalent numbers are subtracted it would yield 0.

Answer 8

"the park sold 8 times as many kid tickets as adult tickets"
This can be translated to, as @DuarteME said,
8a=k, wherein a=adult and k=kid
Subtract k
8a-k=0

Answer 9

25 is referring to the price of the tickets. The variable refers to the number of adults/kids. So you can't plug in 25.

Answer 10

If you don't like the subtraction, then look at the equation as \(k = 8a\).
Notice that \(a\) and \(k\) refer to the \(\underline{\textrm{number}}\) of tickets, as opposed to their \(\underline{\textrm{price}}\).
Say that only one adult went to the park. Then \(a = 1\). Since they sold 8 times as many kid tickets as adult tickets, then \(k = 8 \times 1 = 8\), so 8 kids went to the park, as required.

Answer 11

You have:
\(8a - k = 0.\)
Add \(k\) to both sides:
\(8a - k + k = k.\)
Simplify:
\(8a = k.\)
You only need to change the sign, like I did.