1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nika2105 [10]
3 years ago
9

1. Dorothy bought a teddy bear and sold it at a 20% profit to Kim. Kim bought a suit costing $100 and dressed the teddy bear up

in the suit. Kim then sold the teddy bear in the suit to Karen for $442. Kim made a profit of 30%. How much did Dorothy pay for the teddy bear?​ And why?
2. If x is less than y by 25%, then y is more than x by __%? And why?
Mathematics
1 answer:
makkiz [27]3 years ago
6 0

1. Dorothy paid $200 for the teddy bear

2. y is more than x by 33\frac{1}{3} %

Step-by-step explanation:

1. The given is:

  • Dorothy bought a teddy bear and sold it at a 20% profit to Kim
  • Kim bought a suit costing $100 and dressed the teddy bear up in the suit
  • Kim then sold the teddy bear in the suit to Karen for $442
  • Kim made a profit of 30%

We need to find how much Dorothy paid for the teddy bear

Assume that Dorothy bought a teddy bear for $x

∵ Dorothy bought a teddy bear for $x

∵ She sold it at a profit 20% to Kim

By using the ratio method

→  Buying price    :    Profit    :    Selling price

→  100%                 :   20%       :    120% ⇒ (100% + 20%)

→  x                         :                 :    ?

By using cross multiplication  

∴ 100% × Selling price = x × 120%

- Divide both sides by 100%

∴ Selling price = 1.2x

∴ Dorothy sold the teddy bear for $1.2x to Kim

∵ Kim bought a suit costing $100 and dressed the teddy bear

  up in the suit

∴ The cost of the teddy bear = 1.2x + 100

∵ Kim sold the teddy bear in the suit to Karen for $442

∵ Kim made a profit of 30%

By using the ratio method

→  Cost price    :    Profit    :    Selling price

→  100%             :   30%      :    130% ⇒ (100% + 30%)

→  1.2x + 100     :                 :    442

By using cross multiplication  

∴ (1.2x + 100) × 130% =  100% × 422

- Divide both sides by 130%

∴ 1.2x + 100 = 340

- Subtract 100 from both sides

∴ 1.2x = 240

- Divide both sides by 1.2

∴ x = 200

∴ Dorothy bought the teddy bear for $200

Dorothy paid $200 for the teddy bear

2. The given is:

  • x is less than y by 25%
  • Then y is more than x by how many percent

Assume that y is 100%

∵ y = 100%

∵ x is less than y by 25%

∴ x = 100% - 25%

∴ x = 75%

- The percentage of increasing of y = \frac{y-x}{x} × 100%

∵ The percentage of increasing of y = \frac{100-75}{75} × 100%

∴ The percentage of increasing of y = \frac{25}{75} × 100%

∴ The percentage of increasing of y = \frac{1}{3} × 100%

∴ The percentage of increasing of y = 33\frac{1}{3} %

y is more than x by 33\frac{1}{3} %

Learn more:

You can learn more about the ratio in brainly.com/question/4713715

#LearnwithBrainly

You might be interested in
Solve for the variable x.
inna [77]

Answer:

<u>x = 5</u>

Step-by-step explanation:

Equating the terms :

  • x + 3 = 2x - 2

Add 2 on both sides :

  • x + 3 + 2 = 2x - 2 + 2
  • x + 5 = 2x

Subtract x from both sides :

  • x + 5 - x = 2x - x
  • <u>x = 5</u>
3 0
1 year ago
Write an equation of a line parallel to y = 5x + 4 that passes through (-1, 2)
nikitadnepr [17]

The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7

Step-by-step explanation:

The parallel lines have:

  • Same slopes
  • Different y-intercepts

The form of the linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y = 5x + 4

∴ m = 5 and b = 4

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = 5

- Substitute the value of the slope in the form of the equation

∴ y = 5x + b

- To find b substitute x and y in the equation by the coordinates

   of any point on the line

∵ The parallel line passes through point (-1 , 2)

∴ x = -1 and y = 2

∵ 2 = 5(-1) + b

∴ 2 = -5 + b

- Add 5 to both sides

∴ 7 = b

- Substitute the value of b in the equation

∴ y = 5x + 7

The equation of a line parallel to y = 5x + 4 that passes through (-1 , 2) is y = 5x + 7

Learn more:

You can learn more about the equations of the parallel lines in brainly.com/question/9527422

#LearnwithBrainly

5 0
2 years ago
PLZZZ HELP DUE IN 5 MINS
iris [78.8K]

Answer:

{(2, 9), (5, 9), (1, -6), (-5, 5), (2,9), (5,9), (1,−6), (−5,5)}

Step-by-step explanation:

recall that for a function to be valid, every input must give one and only 1 output. (i.e every x-ordinate must have only one unique corresponding y-ordinate)

I have highlighted in bold and underlined the entries for each of the other choices where an x-value gives more than one possible y-value, hence these are not functions. only the first option satisfies this condition:

{(2, 9), (5, 9), (1, -6), (-5, 5), (2,9), (5,9), (1,−6), (−5,5)} Every x-value has a unique y-value, so it is possible that this is a function.

{<em><u>(6, 6)</u></em>, <em><u>(6, 8)</u></em>, (-8, -7), (-3, -8), (6,6),(6,8),(−8,−7),(−3,−8)}  (not a function)

{(1, 8), (9, -3), <u><em>(7, -4)</em></u>, <u><em>(7, -6)</em></u>, (1,8),(9,−3),(7,−4),(7,−6)} (not a function)

{<u><em>(-5, -1)</em></u>, (-3, -7), <u><em>(-5, 3)</em></u>, (-7, -4), (−5,−1),(−3,−7),(−5,3),(−7,−4)} (not a function)

4 0
2 years ago
Theo buys 5 packages of paper. There are 500 sheets of paper in each package. How many sheets of paper does Theo buy?
anzhelika [568]
Theo buys 2,500 sheets of paper
3 0
3 years ago
Read 2 more answers
Jennifer earned $1000 babysitting over the summer. She spent $250 of her earnings on new clothes. What percent of her earnings d
emmainna [20.7K]

Answer:

25%

Step-by-step explanation:

she earned $1,000

she spent $250

250/1000 = 0.25

0.25 x 100 = 25%

4 0
2 years ago
Read 2 more answers
Other questions:
  • What are the x and y-intercepts of the line described by the equation?
    14·2 answers
  • Factor the expression completely:<br> x³ - 3x² - 4x + 12
    15·1 answer
  • A rectangular garden has a length that is five less than twice the width. the garden perimeter is 50 meters. what are the dimens
    13·1 answer
  • What is the distance between (8, 4) and (8, -6)?<br> 3 units<br> 2 units<br> 10 units<br> 12 units
    6·2 answers
  • What is the solution to this system of equations? Y= 2x - 3.5 x - 2y = -14
    13·2 answers
  • Let A = {101, 202, 303, 404, 505} and B = {101, 404}. What is A ∩ B?
    11·2 answers
  • (2x+2x)+(5x+5x)+(1+1) simplified
    12·1 answer
  • Translate and solve: −5 times b is no less than −35.
    8·1 answer
  • Write 0.25x+1y=12 in slope-intercept form.
    8·1 answer
  • Use the parabola tool to graph the quadratic function f(1) = x² + 100 + 24 Graph the parabola by first plotting its vertex and t
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!