Question

The Jurassic Zoo charges $11 for each adult admission and $2 for each child. The total bill for the 233 people from a school trip was $1069. How many adults and how many children went to the zoo?

Answer 1

so far i did x+y=233
then 11x+2y=1069

Answer 2

what do i do next?

Answer 3

@SerenityJustice74 @ace-n-it @Scooby6363

Answer 4

@HyperPiper

Answer 5

@ganeshie8

Answer 6

you have the correct equations set up

x = # of adults
y = # of children

Answer 7

here's what I'd do

first solve for y in x+y=233

x+y=233
x+y-x=233-x
y = 233 - x

I subtracted x from both sides

with me so far?

Answer 8

yes i am

Answer 9

ok then we will plug that into the other equation

Answer 10

so what would it be

Answer 11

11x+2y=1069

11x+2( y )=1069

11x+2( 233 - x )=1069 ... notice how I replaced `y` with `233 - x`

do you see how the substitution got rid of all the y terms? and how we have nothing but x left?

Answer 12

this replacement is possible because y = 233 - x. Basically saying y and 233-x are the same thing

Answer 13

what do i do from there?

Answer 14

next we distribute the 2 through

11x+2( 233 - x )=1069

11x+2( 233 ) + 2(-x )=1069

11x + 466 - 2x = 1069

what comes next?

Answer 15

9x+466=1069?

Answer 16

yep, then what?

Answer 17

9x=603

Answer 18

good, then there's one more step to solve for x

Answer 19

yea divide by 9 and it becomes x=67

Answer 20

correct x = 67

Answer 21

then you'll use this to find y


x+y=233
67+y=233
y = ????

Answer 22

you subtract 67 frm both sides right??

Answer 23

yep

Answer 24

y=166

Answer 25

so there are 67 adults and 166 children

Answer 26

check:


x+y = 233
67+166 = 233
233 = 233 ... works


11*x + 2*y = 1069
11*67 + 2*166 = 1069
737 + 332 = 1069
1069 = 1069 ... works


both equations are true when (x,y) = (67, 166) so the solution is confirmed