Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101.
Show your steps.

Find the smallest pair of $4$ -digit numbers such that the difference between them is $303$ and their HCF is $101$ . Show your steps.

View step-by-step help

View step-by-step help

Complementary angle identities

Full solution

Q. Find the smallest pair of

4

-digit numbers such that the difference between them is

303

and their HCF is

101

. Show your steps.

Identify Numbers: Since the HCF of the two numbers is $101$ , both numbers must be multiples of $101$ . Let's denote the smaller number as $101a$ and the larger number as $101b$ , where $a$ and $b$ are integers.
Set Up Equation: The difference between the two numbers is given as $303$ , which is also a multiple of $101$ (since $303 = 101 \times 3$ ). We can set up the equation $101b - 101a = 303$ to find the relationship between $a$ and $b$ .
Solve for Relationship: Dividing both sides of the equation by $101$ , we get $b - a = 3$ . This means that the two integers $a$ and $b$ must be $3$ units apart.
Find Smallest $a$ : Since we are looking for the smallest $4$ -digit numbers, we want to find the smallest possible value for $a$ such that $101a$ is a $4$ -digit number. The smallest $4$ -digit number is $1000$ , so we need to find the smallest integer $a$ such that $101a \geq 1000$ .
Calculate Minimum $a$ : Dividing $1000$ by $101$ , we get approximately $9.9$ . Since $a$ must be an integer, the smallest possible value for $a$ that makes $101a$ a $4$ -digit number is $10$ .
Determine Values of $a$ and $b$ : Now that we have $a = 10$ , we can find $b$ by adding $3$ to $a$ , giving us $b = 10 + 3 = 13$ .
Calculate Numbers: The two numbers are therefore $101a = 101 \times 10 = 1010$ and $101b = 101 \times 13 = 1313$ .
Verify Solution: We check that the difference between the two numbers is $1313 - 1010 = 303$ , which matches the condition given in the problem.

More problems from Complementary angle identities

Question

\cos(\theta)=\frac{8}{17}

0^\circ<\theta<90^\circ

\sec(\theta)

? Write your answer in simplified, rationalized form.

\sec(\theta)=

Posted 2 months ago

Question

\cos(x) = -0.3

\sin(90^\circ - x)

Posted 2 months ago

Question

\csc(\theta) = \frac{17}{8}

0^\circ < \theta < 90^\circ

\tan(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

\tan(\theta) =

\newline

Posted 2 months ago

Question

Is the sine function even or odd?

\newline

\newline

\text{[A]even}

\newline

\text{[B]odd}

Posted 2 months ago

Question

Write the sentence as an equation.

\newline

89

is equal to the quotient of

y

17

\newline

/

) if you want to use a division sign.

\newline

Posted 1 month ago

Question

Write the sentence as an equation.

\newline

45

is equal to the quotient of

z

5

\newline

/

) if you want to use a division sign.

\newline

Posted 3 months ago

Question

h

\newline

h^2 + 24h = 0

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

Posted 3 months ago

Question

h^2 - 4h = 0

Posted 1 month ago

Question

Combine the like terms to create an equivalent expression:

\newline

-k-(-8k)=\square

Posted 4 months ago

Question

Which of the following degree measures is equal to

5 \pi

\newline

(The number of degrees of arc in a circle is

360

. The number of radians of arc in a circle is

2 \pi

\newline

1

\newline

144^{\circ}

\newline

900^{\circ}

\newline

1,080^{\circ}

\newline

1,800^{\circ}

Posted 1 month ago