A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax?

A+b=180 A=-2x+115 B=-6x+169 What is the value of B?

natulia [17]

The answer is: " 91 " .
___________________________________________________
→ " B = 91 " .
__________________________________________________

Explanation:
__________________________________________________
Given:
__________________________________________________
" A + B = 180 " ;

"A = -2x + 115 " ; ↔ A = 115 − 2x ;

"B = - 6x + 169 " ; ↔ B = 169 − 6x ;
_____________________________________________________
METHOD 1)
_____________________________________________________
Solve for "x" ; and then plug the solved value for "x" into the expression given for "B" ; to solve for "B"
_____________________________________________________

(115 − 2x) + (169 − 6x) =

115 − 2x + 169 − 6x = ?

→ Combine the "like terms" ; as follows:

+ 115 + 169 = + 284 ;

− 2x − 6x = − 8x ;
_________________________________________________________
And rewrite as:

" − 8x + 284 " ;
_________________________________________________________
→ " - 8x + 284 = 180 " ;

Subtract: "284" from each side of the equation:

 → " - 8x + 284 − 284 = 180 − 284 " ;

to get:

→ " -8x = -104 ;

Divide EACH SIDE of the equation by "-8 " ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ -8x / -8 = -104/-8 ;

→ x = 13
__________________________________________________________
Now, to find the value of "B" :
__________________________________________________________
 "B = - 6x + 169 " ; ↔ B = 169 − 6x ;

↔ B = 169 − 6x ;

= 169 − 6(13) ; ===========> Plug in our "solved value, "13", for "x" ;

= 169 − (78) ;

= 91 ;

 B = " 91 " .
__________________________________________________
The answer is: " 91 " .
____________________________________________________
→ " B = 91 " .
____________________________________________________
Now; let us check our answer:
____________________________________________________
→ A + B = 180 ;
____________________________________________________
Plug in our "solved answer" ; which is "91", for "B" ; as follows:
________________________________________________________

→ A + 91 = ? 180? ;

↔ A = ? 180 − 91 ? ;

→ A = ? -89 ? Yes!
________________________________________________________
→ " A = -2x + 115 " ; ↔ A = 115 − 2x ;

Plug in our solved value for "x"; which is: "13" ;

" A = 115 − 2x " ;

→ A = ? 115 − 2(13) ? ;

→ A = ? 115 − (26) ? ;

→ A = ? 29 ? Yes!
_________________________________________________
METHOD 2)
_________________________________________________
Given:
__________________________________________________
" A + B = 180 " ;

"A = -2x + 115 " ; ↔ A = 115 − 2x ;

"B = - 6x + 169 " ; ↔ B = 169 − 6x ;

→ Solve for the value of "B" :
_______________________________________________________
A + B = 180 ;

→ B = 180 − A ;

→ B = 180 − (115 − 2x) ;

→ B = 180 − 1(115 − 2x) ; ==========> {Note the "implied value of "1" } ;
__________________________________________________________
Note the "distributive property" of multiplication:__________________________________________________ a(b + c) = ab + ac ; AND:
a(b − c) = ab − ac .________________________________________________________
Let us examine the following part of the problem:
________________________________________________________
→ " − 1(115 − 2x) " ;
________________________________________________________

→ " − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;

= -115 − (-2x) ;

= -115 + 2x ;
________________________________________________________
So we can bring down the: " {"B = 180 " ...}" portion ;

→and rewrite:
_____________________________________________________

→ B = 180 − 115 + 2x ;

→ B = 65 + 2x ;
_____________________________________________________
Now; given: "B = - 6x + 169 " ; ↔ B = 169 − 6x ;

→ " B = 169 − 6x = 65 + 2x " ;
______________________________________________________
→ " 169 − 6x = 65 + 2x "

Subtract "65" from each side of the equation; & Subtract "2x" from each side of the equation:

→ 169 − 6x − 65 − 2x = 65 + 2x − 65 − 2x ;

to get:

→ " - 8x + 104 = 0 " ;

Subtract "104" from each side of the equation:

→ " - 8x + 104 − 104 = 0 − 104 " ;

to get:

→ " - 8x = - 104 ;

Divide each side of the equation by "-8" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ -8x / -8 = -104 / -8 ;

to get:

→ x = 13 ;
______________________________________________________

Now, let us solve for: " B " ; → {for which this very question/problem asks!} ;

→ B = 65 + 2x ;

Plug in our solved value, " 13 ", for "x" ;

→ B = 65 + 2(13) ;

= 65 + (26) ;

→ B = " 91 " .
_______________________________________________________
Also, check our answer:
_______________________________________________________
Given: "B = - 6x + 169 " ; ↔ B = 169 − 6x = 91 ;

When "x = 13 " ; does: " B = 91 " ?

→ Plug in our "solved value" of " 13 " for "x" ;

→ to see if: "B = 91" ; (when "x = 13") ;

→ B = 169 − 6x ;

= 169 − 6(13) ;

= 169 − (78)______________________________________________________
→ B = " 91 " .
______________________________________________________

6 0

3 years ago

Answer both please man. Or sorry you'll get a 1 star rating. THanks for answering guys!

Nataliya [291]

For the first one,

x = 10.

For the second one,

x = 12

5 0

3 years ago

Read 2 more answers

NEED HELP ASAP!!! What is the interquartile range of the data set? Enter the answer in the box. Key: 1|5 means 15 A stem-and-lea

monitta

To find the interquartile range, you will list the data that is presented in the stem and leaf plot.

Find the median of the data (30.5)

Find the median of the lower half and the median of the upper half.

Subtract these two values.

The data are 20, 25, 30, 30, 31, 40, 41, 49.
27.5 40.5
40.5-27.5 = 13

The interquartile range is 13.

3 0

3 years ago

Read 2 more answers

Please help!! 40 points x

Alika [10]

Answer: x = 7

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

two runners start 30kilometer apart and run toward each other. they meet after 3hours. One Runner runs 2 kilometers per hour fas

belka [17]

Let the slower runners speed be X kilometers per hour.

Then the faster runners speed would be X+2 kilometers per hour.

The formula for distance is Speed times time.

The distance is given as 30 kilometers and time is given as 3 hours.

Since there are two runners you need to add the both of them together.

The equation becomes 30 = 3x + 3(x+2)

Now solve for x:

30 = 3x + 3(x+2)

Simplify:

30 = 3x + 3x +6

30 = 6x + 6

Subtract 6 from each side:

24 = 6x

Divide both sides by 6:

x = 24/6

x = 4

The slower runner ran at 4 kilometers per hour.

The faster runner ran at 4+2 = 6 kilometers per hour.

3 0

3 years ago