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]
2 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]2 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
Write an expression of the sequence of operations described below
snow_lady [41]

Answer:

the answer is: (g-f)-10

8 0
2 years ago
Jack's father is three times older than Jack. Five years ago, the sum of their ages was 34. How old is Jack's father now?.
Allisa [31]

Answer:

jacks father is x

jack is 3x

34 =

5 0
2 years ago
The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. T
Amiraneli [1.4K]

Answer:

60

Step-by-step explanation:

Substitute 50 for y in the formula

5x+10y=800

5x+10*50=800

5x+500=800

5x=800-500

5x=300

x=300/5

x=60

3 0
2 years ago
Read 2 more answers
Please help me graph
Anika [276]
(x, y) = (-3, 4) hope this helps!
6 0
3 years ago
A contractor finds that 3 gallons of paint will cover 375 sq ft of wall area. How much wall area could be covered with 18 gallon
ss7ja [257]
It will cover 2050 square feet
8 0
3 years ago
Other questions:
  • A die with 12 sides is rolled. What is the probability of rolling a number less than 11?
    10·1 answer
  • Which of the following are dimensionally consistent? (Choose all that apply.)(a) a=v / t+xv2 / 2(b) x=3vt(c) xa2=x2v / t4(d) x=v
    13·1 answer
  • Help me find N and get this right​
    9·1 answer
  • Minossoo is training for cross country in the fall. He ran 5 miles east. Then he turned around and ran 4 miles west. Draw and la
    15·1 answer
  • You find one quarter, two dimes ,and two nickels. A. Write the dollar amount as a decimal. B.Write the dollar amount as a fracti
    9·1 answer
  • What is the slope of the line through (2,5) and (-1,2)?
    14·1 answer
  • Can you help me please with my homework​
    13·2 answers
  • Solve for x 2+8-×=24 what is the answer
    14·1 answer
  • Help me on problem k
    8·2 answers
  • P1. if your school makes $0.72 profit on every 6 raffle tickets sold, how much will it make when it sells the 11th ticket
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!