Leah makes $24 per hour for a 40-hour week and time and a half for every hour over 40 hours. If she made $1140 last week, how many overtime hours did she work?

Four less than nine times a number is one hundred twenty-two. Find the original number.
The cost of renting a subcompact car from Super Rental is $20 a day plus 25 cents per mile. How far can Allison drive in one day if she has only $75?

The length of a rectangular field is 50 meters more than twice its width. If the perimeter is 700 meters, find the dimensions of the field.

A wire measures 84 centimeters in length. It is cut into two pieces. The shorter piece is 6 centimeters shorter than the long piece. Find the length of each piece.

Create a real-life problem that involves linear equations and provide a solution to the problem.

If anyone can help with any of these questions I would really appreciate it, it's been a long time since I have had to do this

You're joking? Let's work on this piecemeal.

Leah makes $24 per hour for a 40-hour week. How much is that?

960 lol

How much did Lisa make last week?

1140 lol

God I feel so out of it right now ha ha

How much extra did Lisa make last week?

(But you're so darn cute... )

I sense this is going to take us all night.

Hurry!

Lol I got the first one, it's 5 lol some of the stuff is starting to come back to me ha ha


I am now stuck on number 4 and 6 lol

lol I got the first one, it's 5 lol some of the stuff is starting to come back to me ha ha
Thank God.

I am now stuck on number 4
Draw a picture.

It has to be shown in a equation lol, I tried drawing a picture only to be yelled at ha ha!

It has to be shown in a equation lol, I tried drawing a picture only to be yelled at ha ha!
You can see it better if you draw a picture. Slap the person who yelled at you.

Draw a picture--a rectangle--then note on each side the values assigned.

(I figured it out ten minutes ago.)

It has to be shown in a equation lol, I tried drawing a picture only to be yelled at ha ha!

rectangle - 4 sides, 2 shorter (x) and 2 longer (2x + 50)

Okay I got the picture drawn

perimeter is short side + long side + short side + long side = 700 m.

picture is of a rectangle - 4 sides, 2 shorter (x) and 2 longer (2x + 50)

Ok got it so far(I appreciate the help! :))

Ok got it so far(I appreciate the help! :))
What did you get so far? Name the value for each side.

375 for the length and 275 for the width?

162.5+162.5+137.5+137.5?

375 for the length and 275 for the width?

no

x for each short side
2x+50 for each long side

x + x + 2x + 50 + 2x + 50 = 700 m.

OK so then after I simplify, would it be

x+x+2x+2x=600?

ok so then after I simplify, would it be

x+x+2x+2x=600?

Yes, then solve for x, the short side.

After that, you can calculate the long side, 2x+50.

Tell me your answers.

x+x=300?

I am just trying to see if I'm on the right track lol

x+x=300?

I am just trying to see if I'm on the right track lol
You got derailed.

1x + 1x + 2x + 2x = 600 m.

ADD the x's.

6x=600?

6x=600?
Yes! *kiss* And??

Short side is 100
Longer side is 250?

Short side is 100
Longer side is 250?
YES!!

(Now I remember why I quit teaching. Hope I don't have nightmares tonight.)

To check your work:

100 + 250 + 100 + 250 = what?

700! Thank you so much! It's been so long since I have done this stuff lol, but it's starting to come back to me a bit

700! Thank you so much! It's been so long since I have done this stuff lol, but it's starting to come back to me a bit
Don't forget to put the meters or feet or dollar signs or whatever on the answers.

Lol yep that I remember, I used to get so many points off in school for that ha ha

lol yep that I remember, I used to get so many points off in school for that ha ha
Figure out the next one (about the wire) and tell me your answers.

48 is the longer piece
36 is the shorter piece?

48 is the longer piece
36 is the shorter piece?
x + x-6 = 84 cm.
2x = 84 + 6
2x = 90
x = 45

thus x-6 =??

39!

39!

45 cm. + 39 cm. = 84 cm.

Don't forget the cm.

Is your homework-challenged "friend" with you, or will you connect with this person later?

Yea she is with me lol. She hasn't had math in 10 years ha ha

Yea she is with me lol. She hasn't had math in 10 years ha ha
Does she understand what we did?

Tell me your answer to the Allison rental car one.

Yeah she understands how we got those answers, we had to isolate x to find the answer.

Is it 220mi?

Yeah she understands how we got those answers, we had to isolate x to find the answer.

Is it 220mi?
Yes!!

Is this person Mrs. Romefalls19?

Ha ha yes! She hasn't had a math class since '99

ha ha yes! She hasn't had a math class since '99
Hmmm, I haven't had one since 1964.

You're a teacher though, you cheated lol :p

Your a teacher though, you cheated lol :p
I haven't taught school (math) since the late '70s. After that I taught preschool. I've been a librarian since 1984--and cataloger for fifteen years ('cause I'm darn good with numbers).

What about creating the real-life problem with linear equations?

Lol I just work on computers

For the real-life problem, whip up a word problem for recarpeting your hallway. The problem will be much like the rectangular field one. Use the area dimension of the hallway as a total instead of perimeter, to make it different from the field one.

I have to leave to eat supper, so please post your word problem and the solution and answer. I will check in a half hour or so.

How does this sound?

You are carpeting your hallway and need to know how much carpet to purchase. After measuring you realize that the hallway has a perimeter of 60 feet and that the length is 10 feet more than the width. Find the length of the sides.

The answer is:
x=10
Length of each side is 20
Width of each side is 10

How does this sound?
I'm back.

How was dinner?

You can see it better if you draw a picture. Slap the person who yelled at you.

Draw a picture--a rectangle--then note on each side the values assigned.

(I figured it out ten minutes ago.)

LOL, I just had to read it to figure it out.

ha ha yes! She hasn't had a math class since '99

I hadn't had math since 1980. It slowly comes back. NEvER had to have Algebra until 2004... was totally lost.

How does this sound?

You are carpeting your hallway and need to know how much carpet to purchase. After measuring you realize that the hallway has a perimeter of 60 feet and that the length is 10 feet more than the width. Find the length of the sides.

The answer is:
x=10
Length of each side is 20
Width of each side is 10
How about:

You are carpeting your hallway and need to know how much carpet to purchase. After measuring, you have found that the hallway has a perimeter of 60 feet. The length of the hallway is ten feet more than the width. What are the dimensions of the hallway? How many square feet will you need for carpet?

width = x
length = x + 10
perimeter = x + x + x+10 + x+10 = 60
area = ? (x * x+10) sq ft

Dinner was leftover cold fried chicken from Brown's, a Chicago franchise. Also, Hawaiian Punch on ice and two homemade brownies. *burp*

Width = 10
Length = 20
x=10
Area = 200sq ft?

Width = 10
Length = 20
x=10
Area = 200sq ft?
Yes!!

Thank you so much for all of your help!

Don't forget to solve with these linear equations:

width = x
length = x + 10
perimeter = x + x + x+10 + x+10 = 60
area = ? (x * x+10) sq ft

Yep we did! Now we can relax and spend the night together!

Yep we did! Now we can relax and spend the night together!
But I have other plans. Could you spend it with Mrs. Romefalls instead?

Well played

well played
Have a great evening, and wave to my mom in Hamlin. She's the one in the red dress and standing on the roof of her car waving back.

Ha ha will do.. Enjoy your night!

Wondergirl - must've given you a greenie recently & don't remember...

But I just wanted to say I'm impressed you stuck with this. I can't guarantee staying on here long enough to have a back to forth with someone and therefore work through that much stuff. (In person or on a chat, sure, but not on here.)

Wondergirl - must've given you a greenie recently & don't remember...

But I just wanted to say I'm impressed you stuck with this. I can't guarantee staying on here long enough to have a back to forth with someone and therefore work thru that much stuff. (In person or on a chat, sure, but not on here.)
Thanks, morgaine. You gave me a greenie on 07/15/09.

Romefalls is an AMHD buddy and is from the part of the world that I grew up in, so I took pity on him. And this question has gotten 212 views so far lol.

Should I? Or shouldn't I? Ok, I dare.

The perimeter of a rectangle is given by shorter length + longer length + shorter length + longer length.

If you look well, you can also write it this way:

Perimeter of rectangle = 2 x (shorter length + longer length)

That's a sort of shortcut.

I'll take the 60 perimeter carpet.

Perimeter = 2 (x + x + 10) = 60

That simplifies to x + x + 10 = 30 (you divide both sides by two to get rid of the '2')

That makes 2x + 10 = 30

Then, solving for x gives you 10 for the shorter side, and (x + 10) gives 20 for the longer length.

:)

Should I? or shouldn't I? Ok, I dare.
Yeah, we know. You came too late to the math party.

Sigh, I know. The thing is that, when Rome posted this, it was 1.42 am for me, I was sleeping! Well, that's the big disadvantage of these time differences, lol! :p

Sigh, I know. The thing is that, when Rome posted this, it was 1.42 am for me, I was sleeping! Well, that's the big disadvantage of these time differences, lol! :p
I was just reading about your country. It sounds beautiful, a wonderful place to live!

Okay, your post is the second of its kind of the week. The first was from firmbeliever. Thanks anyway :)

Except that the education system lags behind. I was given a math paper for 11 and 12 yo students of Australia, and that seemed so difficult for me and I thought that the aussies were far 'advanced' in that subject! :eek: And morgaine, and galactus then told me that there were more countries 'far advanced' sigh... :(

Except that the education system lags behind. I was given a math paper for 11 and 12 yo students of Australia, and that seemed so difficult for me and I thought that the aussies were far 'advanced' in that subject! :eek: And morgaine, and galactus then told me that there were more countries 'far advanced' sigh... :(

OK, wait. 11 and 12 yo? You said 11th & 12th grade on the other post, didn't you?

Don't know if you still need this or not... but here's the answers to all 6 with algebraic explanation for reference:

1) Leah makes $24 per hour for a 40-hour week and time and a half for every hour over 40 hours. If she made $1140 last week, how many overtime hours did she work?

You know that the amount that Leah makes per week is a constant in this problem. Since she is working overtime, she's already finished her 40 hours. So, we know that she already made 24 x 40 dollars per week.

We also know that she makes time and a half or 150% for every hour she works overtime. So her wages for working overtime are 1.5 x 24 because 24 is her normal hourly wage and multiplying that by the rate (1.5) gives her overtime wage rate.

But, since she gets that rate every hour she works, and we want to find how many hours of overtime she works, we define the variable "h" as hours of overtime Leah works and multiply it by the rate of 1.5 x 24 to get 1.5 x 24h

The last piece of given information was that she receives 1140 dollars during that week. So, whatever the formula used for computing her wages must be set equal to 1140.

So now, we have enough information to create an equation for this problem:

24 x 40 + 24 x 1.5h = 1140

Simplify to get:

960 +36h = 1140

Add -960 to both sides to get:

36h = 180

Multiply both sides by 1/36 to reveal that:

h = 5

So she worked 45 hours last week and 5 of them were overtime :)

2) Four less than nine times a number is one hundred twenty-two. Find the original number.

Okay, let's call the original number n. Now translate the "key" words in the problem. Less than means subtract. Times means multiply. Is means equals.

To put that in an equation, you get:

9n - 4 = 122

Adding 4 to both sides gets:

9n = 126

Multiplying by 1/9 reveals:

n = 14

So the original number is 14. To check, multiply it by 9 to get 126, then subtract 4 to get 122 :)

3) The cost of renting a subcompact car from Super Rental is $20 a day plus 25 cents per mile. How far can Allison drive in one day if she has only $75?

So the cost no matter what is going to be 20 dollars since she only rented the car for 1 day. Even if she drives 0 miles, she'll still have to pay 20 dollars.

In addition, for every mile she drives, she must pay 25 cents. So the rate is $.25 to keep the units consistent. . 25m will give the cost of driving m miles not including the 20 dollar fee for renting the car.

We also know that she cannot exceed 75 dollars. The largest mileage will be the amount that allows the equation to equal 75. You don't need an inequality here, though if you really wanted to you could... but there's no point in cluttering up the problem.

So the equation is:

20 + .25m = 75

Add -20 to both sides to get:

.25m = 55

Multiply both sides by 4 to find that:

m = 220

So she can drive 220 miles (or less) :)

4) The length of a rectangular field is 50 meters more than twice its width. If the perimeter is 700 meters, find the dimensions of the field.

This one's a little trickier because it requires a systems of linear equations. The first equation relates the side lengths to each other and the second is the formula for perimeter.

Let L = the length of the field.

Let W = the width of the field.

We know that the length is 50 meters plus 2 times the width. So the first equation is:

50 + 2w = L

The second equation is the formula for perimeter. In case you've forgotten:

2L + 2W = Perimeter

Since we know that the perimeter is 700, by substitution:

2L + 2W = 700

Great! We now have 2 equations and 2 unknowns. We can solve them simultaneously now. Here are the 2 equations set up on top of each other:

2w + 50 = L
2L + 2W = 700

(The systems of equations will be displayed without an extra line of white space between them)

You can solve this by elimination or substitution. Personally, I like substitution better, so I'll use that.

We know that L = 2w + 50, so we'll replace L in the second equation with "(2w + 50)" as shown:

2 ( 2w + 50 ) + 2w = 700

Distribute the 2:

4w + 100 + 2w = 700

Combine like terms:

6w + 100 = 700

Add -100 to both sides:

6w = 600

Multiply by 1/6:

w = 100

Now you can substitute for the length:

2W + 50 = L

2(100) + 50 = L

200 + 50 = L

250 = L

So the width is 100 meters and the length is 250 meters :)

5) A wire measures 84 centimeters in length. It is cut into two pieces. The shorter piece is 6 centimeters shorter than the long piece. Find the length of each piece.

Another systems problem. This one could also be done with guess and check or logically, but here's the algebraic solution:

Call the length of one wire n and the other length m.

n + m therefore = 84

and n = m + 6, since one of the wires is 6 cm longer than the other. It doesn't matter whether the 6 is subtracted or added, or even which side it's on. Choose your preferences.

So the systems is:

n + m = 84
n = m + 6

I'm going to use substitution again:

Substituting "(m + 6)" for n in the first equation gives the single equation:

( m + 6 ) + m = 84

This is easily solved:

2m + 6 = 84

2m = 78

m = 39

Since n is 6 cm longer, n = 45.

So the shorter piece is 39 cm and the longer wire is 45 centimeters :)

6) Create a real-life problem that involves linear equations and provide a solution to the problem.

This one is about as easy as you can get. Do a taxicab problem and model it after the car rental problem. Just substitute the 20 dollar day fee to the base fee for taxi services and the .25 cent rate to whatever you want, then put the amount of money you have on the right side and see how many miles you could ride with that amount of money. Solve it the same way :)