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
WARRIOR [948]
2 years ago
12

Three numbers are in the ratio 2 : 3 : 4 and their sum is 54. If 'x' is the common factor, then the value of 'x' is ________.

Mathematics
2 answers:
Sloan [31]2 years ago
8 0
<h3>Answer:   x = 6</h3>

========================================================

Explanation:

The ratio 2:3:4 scales up to 2x:3x:4x after multiplying all three parts by x.

Their sum is 54, so we can say 2x+3x+4x = 54

Solve for x

2x+3x+4x = 54

9x = 54

x = 54/9

x = 6

------------------

Extra info:

if x = 6, then,

  • 2x = 2*6 = 12
  • 3x = 3*6 = 18
  • 4x = 4*6 = 24

Then notice how 2x+3x+4x = 12+18+24 = 54 to help confirm the answer

Also note how 12:18:24 reduces to 2:3:4 after dividing all three parts by the GCF 6.

Neporo4naja [7]2 years ago
3 0

Answer:

<h3><u>Given</u> </h3>
  • ↦ Three numbers are in the ratio 2 : 3 : 4
  • ↦ The sum of number is 54.
  • ↦ 'x' is the common factor

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

<h3><u>To</u><u> Find</u> </h3>
  • ↦ Value of 'x'

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

<h3><u>Solution</u> </h3>

Let the numbers,

  • ↦ 2x
  • ↦ 3x
  • ↦ 4x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

According to the question,

: \implies\sf{2x + 3x + 4x = 54}

: \implies\sf{9x = 54}

: \implies\sf{x =  \dfrac{54}{9} }

: \implies\sf {x =  \cancel\dfrac{54}{9}}

: \implies\sf{x = 6}

{\dag{\underline{\boxed{\sf{\purple{x = 6}}}}}}

<u>Hence, The value of x is 6.</u>

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Thus numbers are,

  • ↦ 2 × 6 = 12
  • ↦ 3 × 6 = 18
  • ↦ 4 × 6 = 24

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

<h3><u>Verification</u> </h3>

: \implies\sf{2x + 3x + 4x = 54}

  • Substituting the numbers

: \implies\sf{ 12+ 18 + 24 = 54}

: \implies\sf{54= 54}

{\dag{\underline{\boxed{\sf{\purple{LHS=RHS }}}}}}

Hence Proved!!

You might be interested in
After running 10 miles, David drank 2 bottles of water. His brother was thirstier and drank times as much as David. What equatio
bonufazy [111]

Answer:

4 bottles of water

Step-by-step explanation:

4 0
2 years ago
7^1 in expanded form​
In-s [12.5K]

Step-by-step explanation:

{7}^{1}  = 7 \times 1 \\  = 7

8 0
2 years ago
3(5x+2)=2(3x-6)<br> help i need to show work and I have no idea how to do this
tester [92]

Answer: its −2

Step-by-step explanation:

3*(5*x+2)-(2*(3*x-6))=0  

Step by step solution :

STEP

1

:

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  3x - 6  =   3 • (x - 2)  

Equation at the end of step

2

:

 (3 • (5x + 2)) -  6 • (x - 2)  = 0  

STEP

3

:

Equation at the end of step 3

 3 • (5x + 2) -  6 • (x - 2)  = 0  

STEP

4

:

STEP

5

:

Pulling out like terms

5.1     Pull out like factors :

  9x + 18  =   9 • (x + 2)  

Equation at the end of step

5

:

 9 • (x + 2)  = 0  

STEP

6

:

Equations which are never true

6.1      Solve :    9   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

6.2      Solve  :    x+2 = 0  

Subtract  2  from both sides of the equation :  

                     x = -2

One solution was found :

x = -2

8 0
3 years ago
Read 2 more answers
A line passes through the point (2, 10) and has a y-intercept of 4. What is the equation of the line?
KatRina [158]

Answer:

y=3x+4

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when x is equal to 0)

<u>1) Determine the slope (m)</u>

m=\frac{y_2-y_1}{x_2-x_1} where two points that the line passes through are (x_1,y_1) and (x_2,y_2)

We're given the point (2,10) and the y-intercept of 4. Recall that the y-intercept occurs when x is equal to 0. This means that the y-intercept occurs at (0,4), giving us our second point.

Plug these points into the equation

=\frac{10-4}{2-0}\\=\frac{6}{2}\\=3

Therefore, the slope of the line is 3. Plug this into y=mx+b

y=3x+b

<u>2) Determine the y-intercept (b)</u>

The y-intercept is given; it is 4. Plug this back into y=3x+b

y=3x+4

I hope this helps!

3 0
3 years ago
What is the ninth term of the arithmetic sequence defined by the rule below?
Leokris [45]

Answer:

A

Step-by-step explanation:

Substitute n = 9 into the nth term rule

A(9) = - 15 + 2(9 - 1) = - 15 + 2(8) = - 15 + 16 = 1 → A

6 0
2 years ago
Other questions:
  • 0.05% as a fraction in simplest form
    11·1 answer
  • If 52 is 130% of a number, is the number greater or less than 52? Explain.
    14·1 answer
  • How do you solve Diamond problems?
    5·2 answers
  • 2. Find the value of each variable.<br> (1 point)<br> (y + x)<br> 2xx(y-2)
    5·1 answer
  • Which is the graph of F(x)= sqrt 4x
    14·2 answers
  • Helppp meee plssss
    10·1 answer
  • A circle has an area of 28.2743 what is the radius round to the nearest whole number
    7·2 answers
  • Someone please help (urgent)
    5·2 answers
  • “Draw the graph of the line with equation y=3/4x-2”
    12·1 answer
  • En un estadio 6/8 de los asistentes son mayores edad y de estos 2/4 son mujeres ¿que fraccion de los asistentes mayores de edad
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!