Question

Admission to the zoo is $6 for children and $9 for adults. On a certain day, 1480 people go to the zoo and $10,500 is collected.

How many children and how many adults went to the zoo?


children

adults

Answer 1

@AihberKhan

Answer 2

Fairly similar process compared to the last one, but this time you are going to have one system be about the children and adults compared to the total number of people that went and the other system will be about the costs per person compared to the total of money collected.

Answer 3

Do you have any ideas what values we could be using?

Answer 4

no

Answer 5

Well the variables we are looking for are adults and children, correct?

Answer 6

yes

Answer 7

So those two variables will need to be represented by values, and since the easiest is just the first letters in the words, we can use a and c. a and c will be what we have on the left side, but one of the equations is about the number of people and the other is about the cost. In the first, about people, a and c are representing all the people, so if we add a and c, we would get the number of people, yes?

Answer 8

yes

Answer 9

So how would we represent that algebraically? And remember that the total number of people is already known, so we will use an integer for it.

Answer 10

idk

Answer 11

Well we know a+c=total number of people, right? And we are given the total number of people, so you can just put that value in for "total number of people"

Answer 12

How about 6x + 9y = 10,500 in regards to money and
x+y = 1480 in regards to people

Answer 13

Plox no spoilers ):

Answer 14

6 dollars times the number of children
9 dollars times the number of adults
Agreed?

Answer 15

You know what do next michelle?

Answer 16

Buddy, the point is I am trying to lead the asker to what you just said so they can better understand the process of assigning values in a system of equations. I gave them the system of equations last time and now I'm trying to see if they understand WHY, which they don't seem to. You just giving them the system is not helping.

Answer 17

so X is 500 and y is 980?

Answer 18

nah, solve the latter equation for y to get y=1480-x

Answer 19

or x can be 740 and y can be 740

Answer 20

Then plug that into the equation in regards to money.

Answer 21

The thing is that we can do better than guessing if we use substitution

Answer 22

i didnt guess tho i did the math and it could be either one of those if you want to get 1480

Answer 23

10,500 = 6x + 9(1480-x)

Answer 24

Can you solve this for x to find y?

Answer 25

x+y=1480

Answer 26

i already told you what x and y could be

Answer 27

Oh what did you get?

Answer 28

x=740 and y=740 only satisfies one of the equations when both must be accounted for.