All categories

3 years ago

The larger of two numbers is four times the smaller number, and their difference is 18. Find the two numbers.

Mathematics

1 answer:

podryga [215]3 years ago

7 0

Answer:

x = 12 , y = 10

Step-by-step explanation:

Let x , y are two numbers.

x > y

1 ) Three times the greater is 18 times their

difference

3x = 18( x - y )

x = 6( x - y )

x = 6x - 6y

6y = 5x

y = 5x/6 ——-( 1 )

2 ) 4 times the smaller is 4 less than twice

the sum of the two

4y + 4 = 2 ( x + y )

2y + 2 = x + y

y = x -2 ——( 2 )

From ( 1 ) and ( 2 ) ,

5x/6 = x -2

( 5x /6 ) - x = -2

( 5x - 6x ) /6 = -2

-x = -12

x = 12

Put x = 12 in equation ( 2 ) , we get

y = 12 - 2

y = 10

Therefore ,

x = 12 , y = 10

You might be interested in

For which function is f(x) equal to f-1(x)?

Andrews [41]

C...to show this, interchange letters: x = (y+1)/(y-1)xy-x = y + 1xy - y) = x + 1y(x-1) = x+1y = (x+1)/(x-1) ⇐ this is f-1(x) and it's identical to f(x). Note: the equal sign is missing in the definitions of the functions c. & d.

8 0

3 years ago

Pick the correct letter for 6>x A B C D

nevsk [136]

Your correct answer is D

5 0

3 years ago

A recipe calls for 3.75 cups of flour. What is this amount as a mixed number in simples form?

ddd [48]

0.75 is 3/4 and 3 is 3 so the mixed number is 3 3/4

8 0

3 years ago

Read 2 more answers

Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha

Brums [2.3K]

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

$a = 20$ --- tree distance from north gate

$b =14$ --- movement from south gate

$c = 1775$ --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

$AE:DE = AB:CB$

Where:

$AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775$

Substitute these in the above equation

$20:x/2 = 20 + x + 14: 1775$

$20:x/2 = x + 34: 1775$

Express as fraction

$\frac{20}{x/2} = \frac{x + 34}{1775}$

$\frac{40}{x} = \frac{x + 34}{1775}$

Cross multiply

$x *(x + 34) = 1775 * 40$

Open bracket

$x^2 + 34x = 71000$

Rewrite as:

$x^2 + 34x - 71000 = 0$

Expand

$x^2 + 284x -250x - 71000 = 0$

Factorize

$x(x + 284) -250(x + 284)= 0$

Factor out x + 284

$(x - 250)(x + 284)= 0$

Split

$x - 250 = 0 \ or\ x + 284= 0$

Solve for x

$x = 250 \ or\ x =- 284$

x can't be negative;

So:

$x = 250$

6 0

3 years ago

Who is tokugawa shogun??his regime?

KatRina [158]

Answer:

he was a military government of japan.

Step-by-step explanation:

he was known as tokugawa shogunate and also;edo bakufu

4 0

3 years ago