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 Versalia 11-05-2012 05:04 PM

Algebra, Consectutive Integers help.

Hi ggftw ! q-q
So I'm in Algebra I. (Yes 8th grade honors)
And my teacher expects SO much from us,
even though he doesn't teach sh**.

On our homework we have 9 problems, and I have no problem with all of them, except 2 of them.

Effie received a raise at work which meant she was paid \$.75 more per hour this week than last week. Effie worked 18 hours last week, and 14 hours this week. She was paid \$218.50 for the two weeks. Find Effie's hourly rate.
a. last week.
b. this week.

I always feel like they don't give enough information to solve it.
Even though they obviously did. ==

And the last one, is like. Mind blowing.

The country fair lasted three days- Friday, Saturday, and Sunday. On Saturday, twice as many visitors came as on Friday. On Sunday there were twenty more than three times the number of visitors on Friday. 1,700 visitors attended the fair in total. How many visitors were there on:
a. Friday
b. Saturday
c. Sunday

If anyone could help me with any of these,
I'd really appreciate it. x___x.

And if you do, could you show work as to how you did it.
I have to show work, and I have to understand it too.

Thank you I really appreciate it. :py46:

 Math 11-05-2012 05:55 PM

I explained everything I knew step by step because I don't know what you do and don't know.
--
First problem:

Let's put them into variables again.
'x' will be the money earned last week per hour.
'y' will be the money earned this week per hour.

x will stay the same
y will be changed to (x + .75), for each hour earned last week will get an additional +.75 cents.

So now we have x, and y being changed to x + .75. Since y is revised we will not be needing to use it.

"Effie worked 18 hours last week, and 14 hours this week. She was paid \$218.50 for the two weeks. Find Effie's hourly rate."

Let's put this into an equation.
18 x + 14 (x • .75) = \$218.50.

We can't add the 18x+14(x + .75) yet, so let's distribute the 14 to the (x • .75).
18x + 14 (x + .75)
18x + 14x + 10.5
Now we can add.
18x + 14x + 10.5
32x + 10.5
Now let's do the equation since we simplified it.
32x + 10.5 = \$218.50
32x = \$208
x = 6.5

Double checkkkkkkkk
18(6.5) + 14(6.5 + .75)
117 + 14(7.25)
117 + 101.5
218.5

--
Second:

Okay, let's see first. I put Friday, Saturday, and Sunday into variables.
Friday's # of visitors is now 'x'. Saturday is now 'y'. Sunday is now 'z'.

Friday is x. Nothing is changed here.
Saturday is now changed to 2x, because it says that on Saturday, *twice as many visitors came as on Friday*. So it makes sense that it's 2x, right? Two times x, twice as much.
Sunday is now 3x+20. *On Sunday there were twenty more [+20] than three times the number of visitors on Friday[3x].* Twenty more than three times on Friday is 20+3x.

So now we have our 3 variables:
Friday is x.
Saturday is 2x.
Sunday is 3x+20.

Now we just have to use the equation to find "x", which will solve Friday, Saturday, and Sunday.
1,700 = 6x + 20. (6x + 20 is the equations added altogether)
1,680 = 6x
280 = x

x = 280

Now plug it in.
Friday = 280.
Satuday = 2(280) = 560
Sunday = 3(280)+20 = 840+20 = 860.

Always double check your math = 280+560+860 = 1700

 Versalia 11-05-2012 06:12 PM

Thanks Math. <3
I understand that one now.
So just number 8 then.

Thank you again so much. ;o;

 Math 11-05-2012 06:12 PM

Just figured out the first one, will update the last post once I put it in words.
Sorry for double posting, I don't think you'd notice if I smuggled it in there somewhere xD.

 Nebula 11-05-2012 06:18 PM

It appears that you issue is setting up the equations to solve. I will not be giving the full solution however I will slowly guide you through.

To start off we will call the hourly rate of last week x.
So last week she earn \$x an hour. We do not know what x is.
Now. This week she earnt 0.75 more.

So what is 0.75 more than x?
x+0.75

Now just to make sure you understand this first part. Say she got a demotion and earnt \$0.50 less per hour. What would her pay be then?
Spoiler!

And how about if she earn 1.5 times as much?
Spoiler!

And lastly what if her pay rise was \$y more an hour?
Spoiler!

Hopefully you get this concept now. It is fundamental in solving maths problems whether is is for differential equations, area or money.

Now wee need to work out her total earnings for the week.

Week 1 she worked for 18 hours. So how much did she earn? Well you know her hourly rate (x) and how many hours she worked so last week she earnt \$18x.

Now we need to do the same for this week. This one is slightly more complicated but it works the same way. She worked 14hours at a rate of (\$x+0.75) an hour. So the total amount earnt for the week was the numbers of hours times the rate per hour.
Cannyou work that one out?
Spoiler!

It is Really the same logic.

Not we need to do something about these. Well the total pay is this week's pay plus last week's pay. We know the total pay and how much she earnt this week and last week in terms of x.
So can you make an equation for this?

Spoiler!

Now solve that equation for x and then add 0.75 for this week.

Hopefully you can do that :)

 Versalia 11-05-2012 06:32 PM

Thank you Cepheid.
I got
Last week - \$6.50 per hour.
And this week - \$7.25 per hour.

I double checked and it should work.

Thanks so much to everyone who helped me. <3

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