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Sally is buying new school supplies. She used a 15% off coupon on a set of markers that was originally $3.00. She also bought some paper that was 20% off. In total, Sally spent $5.35 after using her coupons. How much was the original price of the paper?

Price she paid for the markers with coupon =   3.00 x .85  = $2.55

Price of paper = P

Price of paper with coupon = .80P

So

2.55 + .80P =  5.35      subtract 2.55 from both sides

.80P = 2.80      divide both sides by .80

P =  2.80 / .80  = $3.50  = original price of the paper

15            13.2

----    =    --------

100             x

Cross Multiply...

15x = 1320

Divide Both Sides By 15

X=88

So 88%

$3 x 0.85 = $2.55 - cost of markers.

Let the original price of paper =P

$2.55 + 0.80P = $5.35

0.80P = $5.35 - $2.55

0.80P =$2.80

P = $2.80 / 0.80

P = $3.50 - Original price of paper.

.15 y = 13.2

y =  13.2/ .15   =  88

Oh wait nvm.

SOLUTION:

We note that j(x) is defined unless one or more of the denominators x+8, x^2+8, x^3+8 is equal to 0.
 

We have x+8=0 if x= -8, x^3+8 and if x= (cube root of -8)= -2. There is no real x for which x^2+8=0. Therefore, the domain of j(x)consists of all real x except and -8 and -2. As a union of intervals, this is...

(-∞ ,-8)∪(-8,-2)∪(-2,∞)

.75N = 24   

N = 24 / .75  = 32

So 1/2 (32)  = 16

$45.67 x 1.08 =$49.32 - cost of the meal + 8% tax.

$49.32 x 1.15=$56.72 - total cost of the meal.

 Using  the log property that

x^x   =   a

x ln (x) = ln (a)

x =  ln (a) / ln (x)      repetitively

                  x

            x

       x

  x            =      2

    x

  x

x      ln(x)    =   ln (2)

      x

   x

x      =    [ ln 2] / [ ln x]

  x

x     ln (x)  =  ln ( ln(2) / [ ln x] )

   x

x      =    ln ( ln(2) / [ ln x] ) / [ ln x ]

x ln (x) =  ln (   ln ( ln(2) / [ ln x] ) / [ ln x ] )

x = ln (   ln ( ln(2) / [ ln x] ) / [ ln x ] ) / ln (x) 

This would...of course.....not be easy to evalute algebraically.....but....

WolframAlpha shows the solution ≈ 1.4466014....

310 /135 =2.2963 -1 x 100 =129.63% - profit as a percentage of the original cost.

 0.36 = (12 + x)/(60 + x)                cross multiply
0.36x + 21.60 = 12 + x
21.60 - 12 = x - 0.36x
9.60 =0.64x                                     divide both sides by 0.64
x =9.60 / 0.64
x = 15 - number of consecutive hits.

\(\dfrac{7.65-4.50}{4.50} = 0.7 = 70\%\)

answer is -2,

I don't have a simple answer yet.

Brute force works.

\(\frac{108}{100}*43000=46440.\)

78  (1 + .45) =  78 (1.45) =   $113.10  ≈  $113  [ rounded ]

4 is good

3 is extraneous because it makes an original denominator = 0

35 = P (.035)(1)     where P is the amt deposited

35 =  P (.035)

P =  35 / (.035)   ⇒    "b"

BTW... P  =  $1000

Let (x + 14) = a

Let 7 = b

So...we have

(x + 14)^2 - 7^2  =

a^2 - b^2  =

(a + b) ( a - b)   =

[ ( x + 14 ) + 7 ]  [ (x + 14) -  7 ]  =

[ x + 21 ] [ x + 7 ] 

Thanks tertre.....I'm going to have to remember that formula!!!!

Let the number of strawberry sold = x

The number of vanilla =  strawberry + 2  =  x + 2

The number of chocolate =  vanilla + 11  =   (x + 2) + 11  =  x + 13

So we have that

x + ( x + 2) + ( x + 13)  = 42     simplify

3x + 15  = 42           subtract 15 from both sides

3x  =  27          divide both sides by 3

x = 9  =  strawberry sold

We can solve by cross- multiplying....but.....we have to remember to reject any solutions that will make any  original denominator = 0 ......

There has to be rational values on either side of the equal sign.

The shortened version of the formula is: \(|30H-5.5M|\), where \(H\) stands for hours and \(M\) stands for minutes. Thus, we have \(|30(6)-5.5(48)|=|180-264|=\boxed{84}\) degrees.

I'll do the first one.....If you have trouble with the rest...let me know

First  a    " ≥ "  or a " ≤ "     means a solid line

While a  " >"  or a "< "   means a dashed line

The easiest way to do this is to graph these lines

y = 2x - 1      and y = -3

So....look at the graph here  :   https://www.desmos.com/calculator/hk7nfsdyrr

The two lines split the grah into 4 quadrants

Picking a point in each quadrant I've selected  (0, 0)  (-2, - 4)   (0, - 4)   (2, 0)

Put each set of coordinates into the original inequalities

If you do this....you will note that the point  (2,0)  is the only point that makes both inequalities true....

So.....we shade like this : https://www.desmos.com/calculator/6fzq3zdgcz

It must be that    x + 9 is the longest side since the longest side of a triangle is opposite the largest angle

So

x + 9 > 3x               

9 > 2x

9/2 > x

And   x + 9 will always be greater than x + 4

But we also  have the restriction (by the Triangle Inequalty) that

3x + (x + 4) > x + 9

4x + 4 > x + 9

3x > 5

x > 5/3

So....the allowable values for x that make x + 9  the longest side  are

5/3 < x < 9/2

Always good to see we got the SAME answers!    Sometimes, I do the work on paper, submit my answer and THEN sign in.....and you may not see I was working on it.....no worries ! 

   I sometimes submit an answer that someone else is working on because there are multiple ways to answer them....and it is good to see them all....

~EP