Question

A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each adult. If the family does not want to spend more than $30 an hour at the health club, create a graph that best models the situation.

Answer 1

well we have two quantities, the the total amount spent, and the maximum they can spend
the total amount spent is going to be

totalCost = costOfKids + costOfAdults

and we want the total cost less than $30, so

totalCost <= $30

can you write this as an equation?

Answer 2

*involving x and y I mean

Answer 3

would it be $30=x+y

Answer 4

not quite
x and y are the *hourly* rates
so we need another variable, t, to represent the time passed
then xt=costOfKids

make sense?

Answer 5

i think so

Answer 6

x is in dollars per hour, so dollars per hour times number of hours is how many dollars

Answer 7

so what is an expression for the cost of the parents?

Answer 8

would it be $30=xy

Answer 9

no, that would just be multiplying the two rates together
if your boss pays you $5/hour, and pays your friend $6/hour, do you make $30 ?
I don't think so

how much you make depends on the time you work

Answer 10

the cost for an hourly service is (price per hour) x (number of hours) = total price

Answer 11

for the kids, it will be
(rate for kids) x (time) = cost of kids
or
xt

for the adults it will be
(rate for adults) x (time) = cost of adults
how can you express this in symbols?

Answer 12

3y=xt

2x=xt ??

idk im so stupid with math lol

Answer 13

no, x is the rate for the kids
im just asking about the cost for the parents
(rate for parents) x (time) = cost for parents
what is the rate for the parents?

Answer 14

wait whats the time?

Answer 15

t

Answer 16

2x=t ?

Answer 17

where did you get the 2 from?

Answer 18

theres 2 adults

Answer 19

let's just think about each adult first
what is the cost of *one* adult?

Answer 20

idkkkkk

Answer 21

it is
(rate for adults) x time
what is the rate for adults?

Answer 22

it doesnt say!!

Answer 23

it does say - y

Answer 24

$y an hour is the rate for adults

Answer 25

oh

Answer 26

omg i dont know what you mean tho !

Answer 27

cost of adult = (rate for adult) x time
rate for adult = y
time = t

Answer 28

so
cost of adult = ????
(in terms of y and t)

Answer 29

y * t=cost of adults

Answer 30

good, that is the cost of one adult
how much then, is the cost of two adults?

Answer 31

2y = cost of two adults ?

Answer 32

great!
how about the cost of the kids now?

Answer 33

oh wait you forgot the time

Answer 34

what is the cost of two adults again?

Answer 35

2y * t =cost of two adults

Answer 36

ok cool
now what about the cost of the kids?

Answer 37

x * t= cost of kids ?

Answer 38

that is the cost of one kid
how many kids are there?

Answer 39

3x * t= cost

Answer 40

great, so the total cost of kids and adults is what?

Answer 41

2y * 3x * t = $30 ?

Answer 42

to find the total of two things you add them, not multiply

Answer 43

2y +3x+t=$30 ?

Answer 44

well it turns out that $30 is the maximum *rate* they want to spend, so we don't need to consider the time anymore
so you don't need t

Answer 45

oh ok so just 2y+3x=$30

Answer 46

almost, except it says they want to spend *no more than* $30 per hour
so it shouldn't be =, but rather...?

Answer 47

ok 2y + 3y < 30

Answer 48

close,\[2x+3y\le30\]if it said that they wanted to spend *less than* 30 an hour you would use <, but they said *no more* than 30 an hour

Answer 49

oh i got x and y mixed up

Answer 50

3x+2y<=30

Answer 51

yeah thats what i meant

Answer 52

thamk youu!!