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
blondinia [14]
2 years ago
5

How many positive integers less than 1000 are 6 times the sum of their digits ?.

Mathematics
1 answer:
Grace [21]2 years ago
4 0

Only 1, 54.

There are obviously no such 1-digit numbers (1 - 9).

Let n = ab be a 2-digit number whose value is 6 times its digit sum, meaning

n = 10a + b = 6 (a + b)

Then

10a + b = 6a + 6b

4a = 5b

Now, 4 and 5 are coprime, so for equality to hold, a must be a multiple of 5 and b must be a multiple of 4.

The only valid multiple of 5 is 5 itself:

• a = 5   ⇒   5b = 20   ⇒   b = 4

There are 2 multiples of 4 to check. The first one gives the same result as a = 5.

• b = 8   ⇒   4a = 40   ⇒   a = 10

but a must be 1-digit.

So among the 2-digit numbers, only 1 such number exists, n = 54.

Let n = abc be a 3-digit number satisfying the criterion. Then

n = 100a + 10b + c = 6(a + b + c)

100a + 10b + c = 6a + 6b + 6c

94a + 4b = 5c

c must be a number from 1-9, which means at most 5c = 5•9 = 45.

If we take the smallest possible values of a and b, we have

94•1 + 4•0 = 94

but the smallest value of 94a + 4b is larger than the largest value of 5c.

So there are no such 3-digit numbers.

You might be interested in
In a certain year, the price of gasoline rose by 20% during January, fell by 20% during February, rose by 25% in March, and fell
satela [25.4K]

Using decimal multipliers, it is found that the value of x is of 16.67.

<h3>What is a decimal multiplier?</h3>

Increases of a% or decreases of a% re represented by decimal values, as follows:

  • The equivalent multiplier for an increase of a% is given by: \frac{100 + a}{100}
  • The equivalent multiplier for an decrease of a% is given by: \frac{100 - a}{100}

In this problem:

  • The price at the beginning of January was of a.
  • Increase of 20% in January, hence 1.2a.
  • Decrease of 20% in February, hence 1.2(0.8)a.
  • Increase of 25% in March, hence 1.2(0.8)(1.25)a.
  • Decrease of x% in April, hence 1.2(0.8)(1.25)\left(\frac{100 - x}{100}\right)a

The price of gasoline at the end of April was the same as it had been at the beginning of January, hence:

a =1.2(0.8)(1.25)\left(\frac{100 - x}{100}\right)a

1.2\left(\frac{100 - x}{100}\right) = 1

\left(\frac{100 - x}{100}\right) = \frac{1}{1.2}

\frac{100 - x}{100} = 0.8333

100 - x = 83.33

x = 16.67

The value of x is of 16.67.

To learn more about decimal multipliers, you can take a look at brainly.com/question/24952336

6 0
2 years ago
A dog is on a 5 ft leash staked to the ground. If he can rotate around the stake, forming a circle, what is the area of the gras
Zanzabum

Answer:

78.5 ft²

Step-by-step explanation:

In this situation, the dog's 5 ft leash is the radius of the circle that he forms.

So, the radius is 5.

Use the area formula, A = \pir². Plug in 5 as r, and 3.14 as \pi

A = \pir²

A = (3.14)(5²)

A = (3.14)(25)

A = 78.5

So, the area of the grass he can cover is 78.5 ft²

7 0
2 years ago
THe equation of the graph line is 2x-3y=12 what is the x-intercept of the graph
katrin2010 [14]

2x-3y=12


Make y substitute 0


2x-3(0)=12


2x= 12


X= 12-2


X= 10


X-intercept is 10

5 0
2 years ago
Helppppppoppp please 10 points !!!
Evgesh-ka [11]

Answer:

2x+27+x+27=180

3x+54=180

3x=180-54

x=126/3

x=42

angle B=x+27

=42+27

=69 degree

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Simplify and evaluate<br><br> (6)(2^3)^2 / (2^2)^2
sveticcg [70]

Simplify and evaluate

(6)(2^3)^2 = 384

(2^2)^2 = 16

5 0
2 years ago
Other questions:
  • Find m <br><br><br><br> A. 50°<br> B. 55°<br> C. 60°<br> D. 65°
    15·1 answer
  • Evaluate the function requested. Write your answer as a fraction in lowest terms. FInd Sin A
    10·2 answers
  • Draw a model to represent the problem 1/2divided by 2/12
    13·2 answers
  • Lesson 10.5 practice A Trigonometry
    7·1 answer
  • Circle A has center of (2, 8), and a radius of 2 and circle B has a center of (5, 4), and a radius of 10. What steps will help s
    11·1 answer
  • How do i solve for x (2x-8)=0
    8·1 answer
  • The midpoint M of CD has coordinates (0,4). Point C has coordinates (0,5). Find the
    9·2 answers
  • Which describes the difference between the two sequences? First Sequence: 1, 6, 36, 216 ... Second Sequence: 3, 6, 9, 12, ... Th
    13·1 answer
  • A [?] degrees<br> B 43°<br> C 15°<br> What is the measure of A?
    12·1 answer
  • It is time my friends...please help me with this image that has haunted me
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!