math algebra equation?

Question

1]a local gym charges nonmembers $10 per hour to use the tennis courts. members pay a yearly fee of $300 and $4 per hour using ghe tennis courts. write and solve an equation to find how many hours you must use the tennis courts to justify becoming a member




2] you are designing a web page for your schools biology club. you want to include photos of the members on the page, which has a width of 640 pixels. you`ve decide that the left and right margin should be 24 pixels each and the space between each picture should be 16 pixels. how wide can each pecture be fit 4 across the width of the pagee.



these are two problems im getting stuck on; do either one. or BOTH xDD mhk thnx

Answer 1

Hello...Ah, word problems ---The kind that many usually gets stuck on. Don't fret!
#1) Read the question over and over again...I don't care if you die or not, just read it over (Well...okay, not that much but you get what I mean)
#2) Then, circle key info and phrases needed for the word problem
a. $10 per h, $300 yearly fee, $4 per hour, JUSTIFY (<----probably the most important word) (sorry, if I used both problems as an example, my hand will fall off. ^_^)
#3) Translate each phrase into numerical format. THINK. Math isn't just doing out number problems, it requires lots of critical thinking and applying of concepts.
Nonmembers: $10 per hour
Okay. Now think of it this way. Let's say for an example, some random nonmember dude went to the local gym and spent 6 hours...Well you'd say "Pshh, easy, he spent $60..." Ha, caughtya, I know you can actually do this. How do you know he spent $60...well you'd say, "$10 * 6...Duh???"
Exactly! the $10 represents the money multiplied by the number of hours. Now think, you don't /really/ know the # of hours given in this problem so the amount VARIES. Therefore, the # of hours will be the variable "x". So --->
10*x or simply 10x.

---Okay, stop, take a break from this tedious message-----

Now, for the members:
You must now make a little mini equation for the total amount of money a member would spend that'd ALWAYS work just like you did with finding an equation for the nonmembers...You may say, "Huh? I made an equation?" My answer: Absolutely.

First "$4 per hour". Refer back to "$10 per hour". Same thing except you change 10x--->4x.
Next $300...Now ask yourself these questions.
#1) Does the required yearly fee vary?
Think logic.....*pause* Of course not...unless the local gym is breaking a contract...
#2) Referring to your answer to question 1, does it need a variable
Of course not.
So leave $300 as just $300. And now just put these together. "
$300 + 4x. These means the whole total charge would be the required yearly charge plus the $4 per hour spent in the gym.

Now the next major major major term. JUSTIFY.
Hmm...Justify.
You can't really solve this problem unless you put the 2 equations together...That's one thing.
So you need an operation/sign that'll ultimately put these equations together.
So which operation does "JUSTIFY" represent?
*
/
+
-
=
You pick...(wisely) Well let's sort this out, multiplication wouldn't make any sense. Division is just nonsense. Addition, well, no because you're not adding the two charges for non/members, subtraction neither. And there you go, Bingo, the equation sign. Now that makes sense. You want to JUSTIFY, meaning you want both equations to equal the same with the SAME quantity of hours.

So
10x=300 + 4x

Perfect, now just do the equation out. (I'm hoping that you know how to do this...*nervous look*)
There are variables on both side. Therefore, to solve the equation, you must leave all the variables on one side and the number on the other to figure it out...
Leaving it to
6x=300
Now, there is multiplication in "6x", use inverse operation "dividing by 6 on both sides" or simply multiply by the inverse of the number A.K.A the reciprocal of 6 which is 1/6, which is basically the same thing as dividing by 6.
That leaves you to
x=50
so 50 hours is the answer. Good luck!

Okay, I'll do the next question just to be nice. XP

Now these kinda questions...Some people will keep staring at this question until they collapse and die and will still not get this. Tip: Draw it out! Just like what Amber had suggested.
#1) Do exactly what I had listed above. Circle and point out key phrases.
640 pixels=width
24 pixels both left and right margin
16 pixels=space between each picture
4 pictures across width

Okay, to clarify confusion. All fo the pixels refer only to width, you will only concentrate on width, nothing else...Capiche??(sp?)

Now with those key phrases in your head, draw the problem out. Make some random rectangle representing the whole web page. Now, first, label the width "640 px". Then, left and right margins...simply draw whatever line from both ends of the rectangle. They should both cut off somewhat amount of width for the space for the photos. Label the gaps "-24 px". Then, draw random 4 boxes within the new width of the web page with spaces between each photo. So you should see 3 gaps in the new web page w/ margins. Label each gap "-16 px"

Okay, now think...
#1) What are you really trying to solve in this problem. Well, you're trying to figure out the width of each photo. So the widthe would be "x". With four equal dimensions photo. You'd get "4x", 4 representing the # of photos w/ same dimension and "x" as the width. If you multiply these two together, you'll get the total width of soley these photos, without the gaps, wihout the margins, nothing. Just these photos. Now, since you're ONLY looking for the total width without margins or spaces, use the info provided. The original width "640" should be subtract by the margins, (24+24=48), and the spaces (16*3=48)
So
640-48-48
Totals 544.
So 544 pixels is the total width with all the photos combined. So NOW you can do the math.
4x=544
(they both equal the same, remember!!!!)
x=136.

Tada. 136 pixels...*phew*

Those who said 144 pixels...not quite, you didn't make a correct equation. I see where you're getting at but it is not correct. #1, You forgot to add in the margins. #2, There will not be 4 16px spaces because the problem never said that the photos at the very far left/right side will have spaces next to the margins. Only between each photos. Drawing will be much clearer... Whoever said 42 for Problem #1, not quite...Read carefully before making an equation. I do not mean to be snobby or insisting, I just don't want the questioner to be confused with all the mix of different answers...

Answer 2

ok let x be the hours...

300+4x=10x

Ok so you would divide and see that you would have to play tennis atleast 30 hours before it was a better deal for you to become a member... 300 divided by 10 would give you 30 then you would break even... then from that point it would be cheaper to be a member and only pay 4 dollars and hour than a non member and pay 10 an hour.

ok second one...

640-48 = 592 for the margins

592-48 = 544 for the space btw the pictures

544 divided by 4 = 136 each picture could be 136 pixels wide...

Answer 3

10x = 300 + 4x. Solve for x. 6x = 300. x = 50 hours.

640 - 24 - 24 - 3(16) = 544 Then divide that by 4 which = 136 pixels each.

It helps if you draw a picture for #2. There are 24 pixels for the left border, then a pic, 16 pixels, and a pic, 16 pixels, and a pic, 16 pixels, the last pic, and then 24 pixels for the border. That's how you get 2 24s and 3 16s.

The question is unclear. Is the distance between each picture 16 pixels or is that the total number of pixels for all the pictures?

Answer 4

10(x)= 300 + 4(x)
subtract 4(x) from both sides
6(x)= 300
x = 50
you must use the tennis courts at least 50 times to justify becoming a member.

to check, plug $50 in each of the x's and both sides will = 200
10(50)= 300 + 4(50)
200 = 200

4(x)+64 = 640
subract 64 from both sides
4(x)= 576
x= 144
each picture can be 144 pixels wide.

to check, plug 144 in each x and both sides will = 640
4(144) + 64 = 640
576+ 64 = 640
640=640

Answer 5

1. 10x=300 + 4x
10x - 4x= 300
6x= 300
x= 300/6
x= 50
so it would take 50 visits for you to justify becoming a member.

2. 640 =24+24+ 16x4+4x
640= 48+64+4x
640= 112 +4x
640-112=4x
528=4x
528/4=x
132=x
each picture is132 pixels

Answer 6

1. you should make these into linear equations.. there is no "starting cost" for non-members so the y-intercept is zero, while members pay $300 to start so the y-intercept for that line is 300.. remember y = mx + b where m is slope and b is the y-intercept.. so for one equation (non-member) you have:

y = mx + 0

and for members you have:

y = mx + 300

to find m you need to plug in some values for x and then calculate the cost.. or, you can just plug in the multiplication values (10 for non-members and 4 for members) to get:

y = 10x for non-members, y = 4x+300 for members...

now solve for when these two equations are equal:
10x = 4x + 300 (solve this for x)
-4x .= -4x
-------------
6x = 300
6x/6 = 300/6
x = 50hrs.

OK, I'll let you struggle a bit with the other one.

Answer 7

1.)Let h stand for the number of hours you play on the tennis court. So the equation would be $300 divided by 10 x h x 4.

2.)I don't get it?!

Answer 8

1)
10x51=510
300+4x51=504
so on your 51 use you would start saving with a membership.
2)
You have 24 pixles on each side so
subtract 640-24x2=592
592/4=148-16x4/3
132 pixles is each picture
Check by adding 132x4+16x4=592
592=592
each picture needs to be 132 pixles wide.

Answer 9

1. Sorry

2. 4x+64=640. Each picture could be 144px wide.

Answer 10

300= 30 hours nonmember

4*30=120 extra dollars

= 12 more hours nonmember

42?

i hope this somewhat helps
what a tough problem
i could be wrong but just putting it out there