Question

HOW DO I SOLVE THIS MEDAL
Donna teaches dance in groups of five students. She rents a hall for the dance classes at $450 per month. She charges $40 per hour per student. Donna teaches four groups of students, and her net earnings per month are $4,350.

Part A: If each student learns dance for the same number of hours, write an equation that can be used to calculate the number of hours each student learns dance in a month. (5 points)

Part B: How many hours did each student learn dance each month? Show your work and justify each step. (5 points)

Answer 1

i think its 450x+40(20)=4350

Answer 2

for part a

Answer 3

hmm well I'm not sure of the answer just yet. But in your equation I don't think the 450x is right. First of all she pays 450 a month so you would want to subtract that from however much money she receives. Secondly, The x is not necessary, We're only dealing with one month here so whats the point in the x?

Answer 4

okay so what should i do

Answer 5

Ok, I'm thinking it should be in this form \[20(40x)-450=4350\]

Answer 6

Does that make sense to you?

Answer 7

i know that theres 4 group of kids and 5 in each so thats 20 kids and she charges 40 for each kid so that would be 800 dollars in total for all the kids

Answer 8

yeah it makes sense

Answer 9

Right. It would be 40 per kid if they all only danced one hour. We right the x to represent number of hours.

Answer 10

Write*

Answer 11

ok im a little confused so the answer for hours would be 6

Answer 12

Thats what I'm getting. Sounds like a reasonable number to me.

Answer 13

okay thanks do you think you could me with some other questions

Answer 14

I can certainly give them a shot.

Answer 15

ok thanks

Answer 16

The table below shows the outputs y for different inputs x:


Input
(x) 1 1 3 3
Output
(y) 4 2 12 6


Part A: Does the table represent y as a function of x? Justify your answer. (5 points)

Part B: The total cost f(x), in dollars, for renting a paddleboat for x hours is shown below:

f(x) = 20 + 10x

What is the value of f(120), and what does f(120) represent? (5 points)

Answer 17

Ok, so in order for something to be considered a function it must pass the vertical line test. Mean that if we put a vertical line on the function at any point it should only go through the function one time. More simply put, if its a function we should have one one y value for every x value. Think about a circle. A circle is NOT a function. If we were to put a vertical line on the function we would get two y values for every x value.

Answer 18

thanks

Answer 19

So based on that, would the given points be part of a function?

Answer 20

so then it doesnt represent y as a function

Answer 21

Right. Because at x=1 we have two y values. Same goes for x=3.

Answer 22

got it so y does not represent x as a function because it doesnt pass through a vertical line

Answer 23

Pretty much. If you're writing an answers a more correct way of putting it would be that the relation does not pass the vertical line test.

Answer 24

A relation is what we call a graph that isn't a function by the way.

Answer 25

ok and for part b what do i do

Answer 26

Part b is super easy. When you're dealing with a function in the form F(x)=9x+23 if you want to find say F(4) just plug 4 in where ever you see an x in the function.

Answer 27

okay and for part c What is the value of f(120), and what does f(120) represent? what do i do there

Answer 28

okay so im guessing i would do f(120)=20 + 10x and just solve it

Answer 29

so the answer would be 10 hrs

Answer 30

Right. Plugging 120 in for every x in the function. As far as what it represents, the question pretty much tells you that. It represents how much is would cost to rent a boat for 120 hours.

Answer 31

ok thanks now this is the second question

Answer 32

Well for one your answer would be an amount of money. It might be helpful to reread the question.

Answer 33

Here, I'll show you how its worked out.

Answer 34

actually im a little confused i put f(120)=20+10x I know that f(120) is the total cost so when i solve it i get 10 hrs for x

Answer 35

is x supposed to equal f(x) like the same number

Answer 36

\[f(x)=20+10x----> f(120)=20+(10)(120)----->f(120)=20+1200---->f(120)=1220\]

Answer 37

Oh it got cut off.

Answer 38

One sec.

Answer 39

ok

Answer 40

\[f(120)=20+1200---->f(120)=1220\]

Answer 41

so x = 10

Answer 42

So you aren't solving for x. All you need to do is plug in 120 for every x in the function. Remember x is equal to the number of hours the boat was rented. Well we were told in the question that that was 120 right?

Answer 43

cuz the question says that f(120) is the total cost and for 20+10x 20 is the fee and 10 is how much they charge per hour so wouldnt it be 10 hrs

Answer 44

cuz 10 times 10 is 100 plus the 20 would equal 120 right