Question

A family went to Hershey Park and paid $12 for each adult and $8 for each child. A group of 15 people went to the park and it cost $160. This system of equations models this situation where x is the number of adults and y is the number of children.
x + y = 15

12x + 8y = 160

How many adults were in the group?

Answer 1

pleaseee helppp!!! i will medal.

Answer 2

Have you considered solving the system?

Answer 3

i tried i just dont understand.

Answer 4

Simplify. Divide the second equation by 4. What do you get?

Answer 5

if i divide 12 by 4 i get 3 and if i divide 8 by 4 its 2. But once i put them in i got 12(3)+8(2)=160 which is not true

Answer 6

ok audrey it is a simple equation :)

Answer 7

12x + 8(15-x) = 120

Answer 8

Why did you do that?

12x + 8y = 160

Divide by 4

3x + 2y = 40

That's all. Don't try to solve up front. Just take one step at a time.

Make sense?

Answer 9

can you see where my equation comes from or do you need me to explain?

Answer 10

i got it. i will tell you my answer once i solve.

Answer 11

oh shoot 160 not 120 my mistake

Answer 12

i copied it wrong just replace the 120 and 160 solve for x and that will be the number of adults

Answer 13

i feel so stupid, how do i solve the equation?

Answer 14

ok dont worry :) ,
so we have 12x + 8(15-x) = 160
12x -8x + 120 = 160
4x = 40
x=10

Answer 15

does that make sense? and if we do 10(12) we get 120 + 8(5) for the kids equals 160

Answer 16

yes, thank you so much!!

Answer 17

happy to help audrey! It makes sense right?

Answer 18

Too bad we don't know if YOU can do it. @MathMan77 did all the work. Why don't you show us one.

Answer 19

good idea!

Answer 20

yes, it makes sence now. what equation?

Answer 21

I will make one up adults cost 10 kids cost 5 we have a group of 6 that spend 50 dollars can you give me the equation?

Answer 22

x + y = 6
10x + 5y = 50
These were supplied in problem above

Answer 23

Please simplify first. It will make your life easier. Divide the second equation by 5. Don't substitute ANYTHING until you have done that.

Answer 24

25? because 10/5 is 2 and 5/5 would cancel, so 2=50 then divide that and get 25??

Answer 25

heres what i do:
we know x is number of adults y is kids and total is 6 so,
x = adults
y(kids) = total(6) - adults(x)
so
y = 6 - x
we put that into the bottom eq with substitution and get...

Answer 26

how do we sub that in? :(

Answer 27

substitute y with (6-x) and distribute