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3 years ago

The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers.

Mathematics

1 answer:

umka21 [38]3 years ago

3 0

Answer:

The two numbers are 15 and 6.

Step-by-step explanation:

Given:

The difference between two numbers is 9.

The first number plus twice the other number is 27.

Now, to find the two numbers.

Let the first number be $x.$

And the other number be $y.$

So, the difference between two numbers is 9.

$x-y=9$

$x=9+y$ ............(1)

As, given the first number plus twice the other number is 27.

According to question:

$x+2y=27$

Substituting the value of $x$ from equation (1):

$(9+y)+2y=27\\9+y+2y=27\\9+3y=27$

Subtracting both sides by 9 we get:

$3y=18$

Dividing both sides by 3 we get:

$y=6.$

The other number = 6.

Now, substituting the value of $y$ in equation (1):

$x=9+y\\x=9+6\\x=15.$

The first number = 15.

Therefore, the two numbers are 15 and 6.

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3 years ago

Vita wants to center a towel bar on her door that is 27 1/2 inches wide. She determines that the distance from each end of the t

timurjin [86]

Answer:

The equation is $x+18 =\frac{55}{2}$ ..

The length of the towel bar is $\frac{19}{2}\ in \ \ \ OR \ \ \ 9\frac{1}{2}\ in$ ..

Step-by-step explanation:

Given,

Length of the door = $27\frac{1}{2}\ in$

we can rewrite $27\frac{1}{2}\ in$ as $\frac{55}{2}\ in$ .

We have to find out the length of the towel bar.

Let the length of towel bar be 'x'

`Since Vita wants that the distance from each end of the towel bar to the end of the door to be 9 inches.

So we can say that the length of the towel bar plus from each end of the towel bar to the end of the door plus from each end of the towel bar to the end of the door is equal to length of door.

framing in equation form, we get;

$x+9+9= \frac{55}{2}\\\\x+18 =\frac{55}{2}$

Hence The equation is $x+18 =\frac{55}{2}$ .

Now we solve the equation we get;

Subtracting both side by 18 we get;

$x+18-18=\frac{55}{2}-18\\\\x=\frac{55}{2}-18$

Now we will make the denominator common we get;

$x=\frac{55}{2} -\frac{18\times2}2= \frac{55}{2} -\frac{36}2 = \frac{55-36}{2}=\frac{19}{2}\ in \ \ \ OR \ \ \ 9\frac{1}{2}\ in$

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2/4=2/2 times 1/2
and remember that 2/2=1 so
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and 1 times anyting is the same so
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