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
Tju [1.3M]
3 years ago
9

The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased b

y 2, the fraction becomes 3/4 . What is the original fraction? Which of the following systems of equations can be used to solve the problem?
A. n + 4 = 3 and d + 5 = 4
B. 3n - 2d = 0 and 4n + 2 = 3d + 2
C. 3n = 2d and 4n + 8 = 3d + 6
Mathematics
1 answer:
masha68 [24]3 years ago
6 0

Answer:

The fraction is \frac{4}{6}

Option (B) is correct.

3n-2d=0  and 4n+8=3d+6

Step-by-step explanation:

Let n denotes numerator and d denotes denominator of the fraction.

Given : The ratio of the numerator to the denominator of a fraction is 2 to 3.

That is \frac{n}{d}=\frac{2}{3}

Cross multiply , we get,

3n=2d

Or, 3n-2d=0   ........(1)

Also, given : . If both the numerator and the denominator are increased by 2, the fraction becomes 3/4

That is \frac{n+2}{d+2}=\frac{3}{4}

Cross multiply , We get,

4{n+2}={3}{d+2}

4n+8=3d+6  .........(2)

3d-4n=2  .......(3)

Thus, from (1) and (2) , option (B) follows.

Solving equation (1) and (3) to get the original fraction using elimination method,

3n - 2d = 0    ............(1)

and 3d - 4n = 2       .........(3)

Multiply equation (1) by 3 , we get ,

9n - 6d = 0  ..........(4)

Multiply equation (3) by 2 , we get ,

-8n + 6d = 4 ..........(5)

Adding (4) and  (5) , we get,

9n - 6d -8n + 6d = 4 + 0

⇒ n = 4

Put n = 4 in (1), we get

3n - 2d = 0 ⇒ 3(4) - 2d = 0 ⇒ 12 -2d = 0  ⇒  12 = 2d ⇒ d = 6

so, the numerator is 4 and  the denominator is 6.

Thus, the fraction is \frac{4}{6}


You might be interested in
Molly ran 2/3 of a mile in 8 minutes if molly rubs at that speed how long will it take. Her to run one mile
dusya [7]

2x/3=8

2x=24

x=12

It takes Molly 12 minues to run one mile.


7 0
3 years ago
A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depen
earnstyle [38]

Answer:

$11988

Step-by-step explanation:

Given that,

The unit cost is given by :

C(x)=0.7x^2-462x+88218

We need to find the minimum unit cost.

For minimum cost,

Put \dfrac{dC}{dx}=0

So,

\dfrac{d}{dx}(0.7x^2-462x+88218)=0\\\\1.4x-462=0\\\\x=\dfrac{462}{1.4}\\\\x=330

Put x = 330 in equation (1).

C(330)=0.7(330)^2-462(330)+88218\\\\=\$11988

So, the minimum unit cost is equal to $11988.

5 0
2 years ago
Explain two different ways to simplify 6/12
deff fn [24]
You can simplify it as...
3/6: Because that's 6/2 and 12/2, so the numerator and denominator recieve the same operations
2/4: Because it's 6/3 which = 2, and 12/4 which = 4
1/2: Because it's 6/6=1 and 12/6=2

I hope this helped! If you have any other questions, just ask, and I hope you have a great day! :)


3 0
3 years ago
Read 2 more answers
Equation or expression ​
marishachu [46]

Answer:

The first is equation the second is expression the third is expression and the fourth is equation

Step-by-step explanation:

equations have equal signs and expressions dont

3 0
3 years ago
Read 2 more answers
Write an expression that evaluates to true if the value of the integer variable number of prizes is divisible (with no remainder
natta225 [31]

Answer:

A=BQ

Step-by-step explanation:

In order to find an expression, you can use the definition of the dividend in a division:

A=BC + R

where A is the dividend, B is the divisor, Q is the quotient (the result of the division) and R is the remainder of the division.

Let A represent the integer variable number of prizes and B represent the integer variable number of participants.

In this case R=0 and B≠0, therefore:

A=BQ

A is divisible by B if A can be written as an integer multiple of B. In other words, you have to find an integer number Q that multiplied by B produces A.

8 0
3 years ago
Other questions:
  • Chico walks 3/5 mile to the library. Nikki walks 1/4 the distance that Chico walks to the library. How far does Nikki walk?
    10·1 answer
  • Enter the value of k in function g(x)
    14·1 answer
  • A producer plans an outdoor concert for the weekend. The cost of the concert is $8,000 which includes advertising, security, pri
    10·1 answer
  • 1/2= how many inches
    15·1 answer
  • For every touchdown scored by the Timberwolves, the mascot does 333 back flips and the cheerleaders set off 666 confetti cannons
    5·1 answer
  • 4/5 of the cake was left, but after Brian ate some only 1/4 of the cake was left. Which fraction of the cake did Brian eat?
    6·1 answer
  • Determining if a Ta<br> Which represents a function?
    11·1 answer
  • 3) From the figure below, give the area of the shaded blue region
    15·2 answers
  • Find the altitude of triangle whose vertex is a(1,-2) and the equation of the base is X+y=3.
    12·1 answer
  • Jamar and Theresa decide to create a new playlist and include a total of ten songs what is the probability that the first two so
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!