Grace works as a salesperson at an electronics store and sells phones and phone
accessories, and makes a fixed commission for each phone sale and a different fixed
commission for each accessory sale. Yesterday Grace sold 18 phones and 21
accessories and made a total commission of $204. Today she sold 6 phones and 14
accessories and made a total commission of $82. Determine the price of each phone
and the price of each accessory.

Grace Works As A Salesperson At An Electronics Store And Sells Phones And Phoneaccessories, And Makes

Answers

Answer 1
We can use a system of linear equations to solve this. I will use the variable P for phones and A for accessories.

Our first equation is: 18P + 21A = 204. This is because she told 18 phones and 21 accessories yesterday which got her $204.

Our next equation is: 6P + 14A = 82. This is because she sold 6 phones and 14 accessories today which got her $82.

We can use elimination to solve this system. We can multiply the equation 6P + 14A = 82 by -3. This is so we can avoid sign errors if we multiply by 3. Our new equation is -18P - 42A = -246.

Next, we add that equation to 18P + 21A = 204. This gives us -21A = -42. Once we solve for A, by dividing by -21, we get A = 2.

Next, we can plug A into our equation. I will plug it into the second one. 6P + 14(2) = 82. This gives us 6P + 28 = 82. Once we get 6P alone, we get 6P = 54. Solving for P gives us 9.

One phone costs $9, and an accessory costs $2.

Related Questions

For all values of x, f(x)=2x+1 and g(x)=x^2. Solve fg(x)=gf(x). (Mathwatch)

Answers

[tex]\text{Given that,}\\\\f(x) = 2x+1,~~ g(x) = x^2\\\\\ \text{now,}\\\\f(g(x)) = g(f(x))\\\\\implies f(x^2) = g(2x+1)\\\\\implies 2x^2+1=(2x+1)^2\\\\\implies 2x^2+1= (2x)^2 +2\cdot 2x + 1\\\\\implies 2x^2 +1 = 4x^2 + 4x +1\\\\\implies 4x^2 -2x^2 +4x +1-1 =0\\\\\implies 2x^2 +4x =0\\\\\implies 2x(x+2)=0\\\\\implies 2x =0~~ \text{or}~~ x+2 =0\\\\\implies x =0 ~~~\text{or}~ x =-2\\\\\ \text{Hence,}~ x =0 ~\text{and} ~ x =-2~ \text{are the solutions.}[/tex]

Describe the graph x = 2.

Group of answer choices

Horizontal line that goes through the point (0,2).

Vertical line that goes through the point (2,0).

Diagonal line that goes through point (0,2).

Diagonal line that goes through the point (2,0).

Answers

Answer:

3rd is the answer!! Hope this helps

Figure ABCD is transformed to obtain figure A′B′C′D′:

A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 4, 1, B prime at 2, negative 1, C prime at 2, negative 4, D prime at 4, negative 2.
Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)

Part B: Are the two figures congruent? Explain your answer. (4 points)

Answers

Answer:

Reflected along x axis

Translated 7 units to the right

Step-by-step explanation:

If a point (x, y) is reflected along the x axis, its x coordinate remains the same and the y coordinate is opposite (negated). The new point is at (x, -y)

If a point (x, y) is translated h units to the right, the new coordinate is (x+h, y).The transformation are as follows:

It is reflected along the x axis so that the new coordinates would be at A1 at (- 4, -4), B1 at (- 2, -2), C1 at (- 2, 1), D1 at (- 4, -1)

It is translated 7 units to the right, The new coordinates are A' at (3, -4), B' at (5, -2), C' at (5, 1), D' at (3, -1)

Hope that's better

change percentage to a decimal
52 %
319%
7.9%
4/5%
3 7/8%
6 2/3%

2.
There are six bottles of water. Each bottle contains 0.65 L of water. The capacity of a cup is 0.26 L.How many cups can you fill with all the water.

3.
30.8 m of cloth is needed to make 7 shirts. What is the length needed to make 16 shirts

4.
Mrs Wong buys 0.6 kg of fish balls for $15. Mr Chan buys 0.5 kg from the same shop how much should he pay?
5.
every 0.35 L of mango drink is made of 0.14 kg of mangoes and some soda . Connie wants to buy 3.75 L of mango drink . How many kilograms of mangoes dose she need

Answers

Answer:

52%=0.52

319%=3.19

7.9%=0.079

4.5%=80

37/8%=4.652

62/3%=20.67

2. 15 cups

3. 70.4m

4. $12.5

5.

Step-by-step explanation:

52%=52/100=0.52

319%=319/100=3.19

7.9%=7.9/100=0.079

4/5%=(4/5)/100=4/5×100=80

37/8%=4.(5/8)=4.652

62/3%=20.(2/3)=20.67

1 bottle holds 0.65L

1 cup holds 0.26L

6 bottles hold (0.65×6) =3.9L

n cups hold 3.9L

0.26n=3.9

n=3.9/0.26

n=15

30.8m make 7 shirts

ym make 1 shirt

7y = 30.8

y = 4.4m

1 shirt needs 4.4m

16 shirts need 16×4.4=70.4m

0.6kg cost $15

1kg costs $b

0.6b=15

b=$25

1kg costs $25

0.5kg cost (25×0.5)=$12.5

Help!! Ill give 100 points if your correct

Answers

[tex]\\ \sf\Rrightarrow 12\dfrac{5}{6}-5\dfrac{1}{6}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{77}{6}-\dfrac{31}{6}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{77-31}{6}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{46}{6}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{23}{3}[/tex]

[tex]\\ \sf\Rrightarrow 7\dfrac{2}{3}[/tex]

Given info:- Subtract and simplify. 12(5/6) - 5(1/6) The given options are (a) 6(1/3) (b) 5(2/3) (c) 7(1/3) (d) 7(2/3)

Solution: 12(5/6) - 5(1/6)

= (72+5)/6 - (30+1)/6

= 77/6 - 31/6

Take the LCM of 6 and 6 is 6.

so,

= (77*1 - 31*1)/6

= (77-31)/6

= 46/6

= (46÷2)/(6÷2)

= 23/3

= 7(2/3) Ans.

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Jerome solved the equation 1 3 x + 5 6 = 1 as shown. 1. Subtraction property of equality: 1 3 x + 5 6 − 5 6 = 1 1 − 5 6 2. LCD: 1 3 x = 1 6 − 5 6 3. Multiply by...

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A grocery store charges $5 for every 3 1/4 pounds of furit. Eleizibeth has 9 3/4 pounds of fruit in her grocery cart. How much will Elizabeth have to pay to purchase the fruit?
Sorry for the spelling :)

Answers

Answer:

15 dollars

Step-by-step explanation:

because f it 9 3/4 and it 5 dollars for every 3 1/4  its like multiplying 3 to 3 1/4 so 15 dollars  :(:

i suck at this stuff
pls help asap
ty <3

Answers

Answer:

12*2=24

Step-by-step explanation:

Jason has $45.00. He wants to buy equal numbers of soft drinks and sandwiches. A soft drink costs $0.79. A sandwich costs $2.49.


Part A


How much does a sandwich and drink cost together?


$



Part B


How many can he buy with $45.00?




soft drinks and

sandwiches


​Part C


How much change will Jason get?


​$

Answers

Answer:

Step-by-step explanation:

How much does a sandwich and drink cost together?

($0.79 + $2.49) = $3.28

How many can he buy with $45.00?

$45/$3.28 = 13.72 or 13 sandwich/soda combos.

 

13 soft drinks and  

13 sandwiches

How much change will Jason get?

$45 - 13($3.28) = $2.36

5ab+8c}​ if a = 3, b = 2, and c = 9.

Answers

Step-by-step explanation:

5ab + 8c

Putting values of a = 3 b = 2 and c = 9

5(3)(2) + 8(9)

30 + 72

102

A farmer decides to make three identical pens with 88 feet of fence. The pens will be next to each other sharing a fence and will be up against a barn. The barn side needs no fence. What dimensions for the total enclosure (rectangle including all pens) will make the area as large as possible?

Answers

Answer:

The long fence, AC = 44 feet

4 shorter segments at 11feet each = 44 feet

Area = 484 ft^2

Step-by-step explanation:

The three pens will share one fence section parallel to the barn, we'll call it AB.  Each pen will need two side fence segments, from the front fence to the barn.  We'll call those portions AC.  We need four of them:  two for the outer sides and two more to divide up the space equally among the three pens.  The total area would be AB*AC.

We know that AC + 4AB = 88 feet.

or AC = (88feet - 4AB)

Area = AB(88feet - 4AB)

Area = 88AB - 4AB^2

To maximize the area, we can take the first derivative and set it equal to zero:

Area' = 88 - 8AB

0 = 88 - 8AB

AB = 11 feet

AC = (88 - 4AB)

AC = (88 - 44)

AC = 44 feet

The fours segments of fence:  

AC + 4AB = 88 feet

(44) + 4(11 feet) = 88feet

Area = 44' x 11 ft' = 484 ft^2

what is 3x + 4y = 10

6x - 4y = 8

Answers

Answer:

x=2

y=1

Step-by-step explanation:

9x+0=18

so it's x=2

6=4y=10

so y=1

What is the greatest common factor of 24 and 9

Answers

Answer:

The Greatest Common Factor of 24 and 9 is 3.

Answer:

3

Step-by-step explanation:

the biggest number u can divide 24 and 9 commonly is 3

Find the value of x.
75
70
60
80

Answers

Answer:

75. is yr correct ans.

Step-by-step explanation:

hope it helps.

stay safe healthy and happy.

Answer:

x = 75

Step-by-step explanation:

The triangle has 2 congruent sides and is therefore isosceles with 2 congruent base angles, both of measure x

The sum of the 3 angles = 180° , that is

x + x + 30 = 180

2x + 30 = 180 ( subtract 30 from both sides )

2x = 150 ( divide both sides by 2 )

x = 75

Can someone please help me with this question

Answers

A. Angle 3 is a vertical angle to angle 2 which means they are the same.

Angle 3 = 76 degrees

B. Angle 6 is also the same as angle 2.

Angle 6 = 76 degrees

C. Angle 8 + angle 6 form a straight line which equals 180 degrees

Angle 8 = 180 - 76 = 104 degrees

Answer:

76° , 76° , 104°

Step-by-step explanation:

(a)

∠ 2 and ∠  3 are vertically opposite angles and are congruent , then

∠ 3 = 76°

(b)

∠ 6 and ∠ 3 are alternate angles and are congruent , then

∠ 6 = 76°

(c)

∠ 6 and ∠ 8 are adjacent angles on a straight line and sum to 180° , then

∠ 8 = 180° - 76° = 104°

CAN SOMEONE HELP ME PLEASE ASAP!?

Answers

Answer:

false

Step-by-step explanation:

Find the missing base.
Write your answer as a whole number.
?^2=36

Answers

Answer:

6

Step-by-step explanation:

6^2 = 36

hope this helps! :D

have a miraculous day!! <3

A bag contains pennies, nickels, nickels, and nickels. There are 50 coins in total. Of the coins, 14% are pennies and 34% are dimes. There are 6 more nickels than pennies. How much money does the bag contain?

Answers

answer:

8 pennies,16 dimes,13 nickels,13 quarters

Step-by-step explanation:

total number of coins = 50

16% are pennies

16% of 50

16/100 x 50=(16x50)/100=800/100=8

Pennies = 8

32% are dimes

32% of 50

32/100 x 50=(32x50)/100=1600/100=16

Dimes = 16

5 more nickels than pennies

Pennies = 8

nickels = 8 + 5 = 13

nickels = 13

8+16+13=37

50 - 37 = 13

13 quarters

pennies = 8, dimes = 16, nickels = 13, quarters = 13

What is 5 rounded to the nearest whole number, explain why

Answers

Answer:

The answer is 10

Step-by-step explanation:

It is

(Exit
Topic 3: Assessment Form C
Hugo's exercise data is shown. Use the trend line y = 3.5x + 10 to complete the sentence.
Laps
7 8 9 10 11
Time (min)
35.5
37
41.5
45
49.5
It will take Hugo about
min to run 6 laps

Answers

Answer:

35.5

Step-by-step explanation:

Estimate the line of best fit using two points on the line.

Answers

Answer:   i think it's b

Answer:

C.

Step-by-step explanation:

A and D are immediately wrong since the line is increasing.

Using the formula of rise over run, we can find the slope. We then use 40 as the rise and 5 as the run

40/5 is 8.

We can now put 8 as the slope in the y=mx+b equation. We can see the line intersect at 20 at the y-axis, which makes 20 the y-intercept. We can now insert that into the b part of the equation. This leaves us with y=8x+20.

Find the zeros of quadratic equation X^2 - 3x + 9 = 5x - 10

Answers

x^2 - 3x + 9 - 5x + 10 = 0

x^2 - 8x + 19 = 0

[tex]x^{2} -3x+9=5x-10 <=> x^{2} -3x-5x+9+10=0\\<=>x^{2} -8x+19=0 <=>x^{2} -2.4+16+3=0\\<=>(x-4)^2+3=0[/tex]

ok done. Thank to me :>

what is the slope of the line tha passes through the points (4,-9) and (8,-3)

Answers

the slope of this line is 3/2

HELP PLEASE WILL GIVE BRAINLIEST

Answers

No one will solve all ten problems for you

you should create a question for each problem

Answer:

In attachment

Step-by-step explanation:

See the attachment.  They are much easier to solve if you set up a spreadsheet template and then copy that template for each problem.  The inputs would be the two given points for each graph.  Problem 3's slope is undefined, since it is a vertical line and the run is 0, no change in x.  Since slope is "Rise/Run," this is dividing by zero, a No-No for mathematicians, as well as us chemists and other mortals.

Adrian, Ben and Charlie share some sweets in the ratio 7.4.11
Charlie got 52 more sweets than Adrian. Work out the total amount of sweets.​

Answers

Answer:

286 sweets.

Step-by-step explanation:

If Adrian had x sweets, Charlie got x+52 sweets.

The number of parts  is 7+4+11 = 22.

So Adrian had 7/22 of the total  and Charlie had 11/22 = 1/2 of the total.

This means that Ben had 4/22 = 2/11 of the total.

If y is the total number of sweets:

y = x + x + 52 + 2y/11

9y/11 = 2x + 52

2x =  9y/11 - 52.............(1)

Also x + 52 = y/2

y = 2x + 104

2x = y - 104...............(2)

Equating (1) and (2) -   (as there is 2x on left side of both equations):-

9y/11 - 52 = y - 104

52 = 2y/11

y = 52 * 11/2

y = 286 sweets.

Gillian can jog 100 metres in 24 seconds. How long will it take her to jog 2 km?

Answers

Answer:

8 minutes or 480 seconds

Step-by-step explanation:

1 km = 1000 m

100x20=2000

24 x 20 = 480

480/60 = 8

Answer:

Step-by-step explanation:

Jae bought 85 tickets to spend on games and rides at an amusement park. Games cost 3 tickets each, and rides cost 8 tickets each. Jae has already used 39 of the tickets. If he uses all of his remaining tickets for rides, how many more times can Jae go on rides?

Answers

Answer:

15

Step-by-step explanation:

Jae can go 15 more times on the rides.

Answer:

Jae can ride 5.75 or 5 more times

Step-by-step explanation:

Total of tickets, Jae buys 85

Jae uses (-) 39 tickets

85 - 39 = 46 remaining tickets

Rides: 8 tickets each

46/8 = 5.75

I hope this helps.

help with my math please

Answers

Answer:

j mmmmmmm

Step-by-step explanation:

mmmmmmmmm

The ratio of taxis to buses to bikes
is 12:5:18.
How many buses are there if there
are 72 bikes?

Answers

Answer:

20 buses

Step-by-step explanation:

Using the given ratio, we can see that for every 12 taxis, there are 5 buses and 18 bikes.

To get from 18 bikes to 72 bikes, we multiply by 4. Therefore, to figure out the number of buses, we multiply it by 4.

5 * 4 = 20

Hope this helps! :D

The first and second terms of an arithmetic sequence are 50 and 100, respectively.
The first and second terms of a geometric sequence are also 50 and 100,
respectively. The sum of the third terms of these two sequences is???

Answers

arithmetic sequence is a constant addition where geometric is a constant multiplication so the third in arithmetic is 150, whereas the geometric third is 200 because 50 = 100 • x and “x” is 2 so it’s 150 + 200 = 350!

kari purchased 3 cherry trees for sale. Each cherry tree cost $9 less than its full price. She paid a total of $135

Answers

Answer:

whats the question?

Step-by-step explanation:

Answer:

each tree was $36

Step-by-step explanation:

if the trees are $9 less then the full price and she purchased 3

9 times 3 is 27 135-27 is 108 so then when you divide 108 and 3 to get $36

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